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function [T,X]=SolvesemiImplctEuler(f,h,X0,n)
X=X0;
T=0;

%Loop to solve by Semi-implicit Euler
for i=1:n
    dX=f(T(end),X(end,:));
    Xn=X(end,:)+h*dX';
    X=cat(1,X,Xn);
    T=cat(1,T,T(end)+h);
end
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      • Illuminate\Cache\Events\CacheHit (175μs)
      • creating: site.layouts.app (525μs)
      • composing: site.layouts.app (26μs)
      • creating: components.canonical (650μs)
      • composing: components.canonical (253μs)
      • creating: components.open-graph (336μs)
      • composing: components.open-graph (95μs)
      • creating: site.headers.header (415μs)
      • composing: site.headers.header (247μs)
      • Illuminate\Cache\Events\CacheHit (2ms)
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      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (407μs)
      • Illuminate\Cache\Events\CacheHit (332μs)
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      • Illuminate\Cache\Events\CacheHit (270μs)
      • creating: components.forms.contact-us (276μs)
      • composing: components.forms.contact-us (154μs)
      • creating: components.forms.get-started (164μs)
      • composing: components.forms.get-started (74μs)
      • creating: components.forms.free-tool-download (128μs)
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      • creating: components.forms.claim-free-worksheet (123μs)
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      • creating: components.forms.tutor-subscription-waitlist (131μs)
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      • creating: components.forms.tutor-subscription-join (179μs)
      • composing: components.forms.tutor-subscription-join (80μs)
      • creating: components.forms.tutor-support (185μs)
      • composing: components.forms.tutor-support (154μs)
      • 316 x Illuminate\Cache\Events\CacheHit (23.6%)
        191ms
        15 x Illuminate\Database\Events\QueryExecuted (4.46%)
        36.10ms
        15 x Illuminate\Database\Events\StatementPrepared (3.94%)
        31.86ms
        6 x Illuminate\Cache\Events\KeyWritten (0.56%)
        4.53ms
        6 x Illuminate\Cache\Events\CacheMissed (0.47%)
        3.84ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.27%)
        2.17ms
        1 x Illuminate\Routing\Events\Routing (0.12%)
        1.00ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.11%)
        876μs
        7 x eloquent.retrieved: App\Models\SubjectCat (0.11%)
        865μs
        1 x creating: components.canonical (0.08%)
        650μs
        1 x eloquent.booting: App\Models\SubjectCat (0.07%)
        560μs
        1 x creating: site.layouts.app (0.06%)
        525μs
        14 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        443μs
        1 x creating: components.breadcrumbs (0.05%)
        420μs
        1 x creating: site.headers.header (0.05%)
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        381μs
        1 x creating: components.open-graph (0.04%)
        336μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        302μs
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        276μs
        1 x composing: components.canonical (0.03%)
        253μs
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        247μs
        1 x creating: homework.show (0.03%)
        240μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
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        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        199μs
        1 x creating: components.forms.tutor-support (0.02%)
        185μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        179μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        175μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)
        167μs
        1 x creating: components.forms.get-started (0.02%)
        164μs
        1 x composing: components.forms.contact-us (0.02%)
        154μs
        1 x composing: components.forms.tutor-support (0.02%)
        154μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        131μs
        1 x composing: components.breadcrumbs (0.02%)
        129μs
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        128μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
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        95μs
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        88μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        81μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        80μs
        1 x composing: homework.show (0.01%)
        78μs
        1 x composing: components.forms.get-started (0.01%)
        74μs
        1 x composing: components.forms.free-tool-download (0.01%)
        70μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        70μs
        1 x creating: components.footer (0.01%)
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      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
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      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
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      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
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      middleware
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      controller
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      where
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      homework.show
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      app/Http/Controllers/HomeworkLibraryController.php:79-176
      15 statements were executed, 4 of which were duplicates, 11 unique. Show only duplicated50.99ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '40550' limit 1
        3.82mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
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        • 1: 0
        • 2: 40550
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (397)
        10.83mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (40550)
        6.72mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.21mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 34
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 40550 and `subject` = 397 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        4.54mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 40550
        • 1: 397
        • 2: published
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        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (397)
        850μstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 40550 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        800μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 40550
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 40550 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        810μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 40550
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 40550 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        5.68mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 40550
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        3.87mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 34
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.73mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        3.92mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        4.17mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.02mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.02mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      14HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\SubjectCat
      7SubjectCat.php
      App\Models\Subject
      2Subject.php
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          request_cookies
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