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Implicit Differentiation help?

asked 2022-01-08 02:41:57 +0100

Rossa625 gravatar image

How can I prove that dy/dx = x^3 + x is equal to y = x^4/4 + x^2/2 + C using SageMath?

I'm interested in merging SageMath and LaTeX together in some way to help with my note-taking skills for college coming up. Thanks!

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Welcome to Ask Sage! Thank you for your question.

slelievre gravatar imageslelievre ( 2022-01-09 07:37:30 +0100 )edit

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answered 2022-01-09 07:41:46 +0100

slelievre gravatar image

Combining SageMath with LaTeX can be done with:

  • SageTeX
  • PythonTeX
  • texsurgery

You could also have a look into TeXmacs and its SageMath package.

To solve the differential equation:

sage: y = function('y')(x)
sage: de = diff(y, x) == x^3 + x
sage: desolve(de, y)
1/4*x^4 + 1/2*x^2 + _C
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Asked: 2022-01-08 02:41:57 +0100

Seen: 119 times

Last updated: Jan 09 '22