Ordinary Differential Equations - SymPy Tutorial 10

This is the tenth video in a new series on SymPy - Symbolic Computations in Python. In this video, we will show you how to solve ordinary differential equations (ODE's) in Python with SymPy.
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▬▬▬▬▬▬ ⏰ Timestamps ⏰ ▬▬▬▬▬▬
00:00 - Introduction
00:39 - Goal
01:17 - Create an ODE
04:20 - Solving the ODE
08:50 - Giving Initial Conditions
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[@rajanalexander4949]

Great video: succinct and clear. Thank you!

[@TMQuest]

You're welcome! Thanks for the nice comment :)

[@blackguardian89]

Very clear explanation, thank you! It's kind of interesting why the conditions are referred to as initial when they are obviously boundary (the first one is Dirichlet BC and the second one - Neumann BC).

[@TMQuest]

Thanks for the feedback. I typically refer to Dirichlet & Neumann boundary conditions when one has a fixed domain where one considers the differential equation. When the DE is posed on the full real line, then I typically use the terminology initial conditions :)

[@profarvind]

Very Clear Explanation, thanks a ton.

[@AJ-et3vf]

Awesome video! Thank you so much!

[@geryonklein9673]

幫助很大，期中報告就靠這部了。

[@direndeniz8817]

Thank you for preparing such useful tutorial for us

[@TMQuest]

No problem :)

[@kennedymwavu]

This is the definition of precise and concise!

[@TMQuest]

Thanks!

[@winckler100]

Very nice video, congrats! And thanks for the explanation.

[@TMQuest]

Thanks!

[@ferdinandedward9411]

thank you so much :D

[@TMQuest]

No problem :)

[@fredesch3158]

Awesome

[@feudiable]

7.54 The free symbols are not always in the same order. Is there a way to prevent this?

[@charliepullen1463]

Thanks for the video! why did you set the constants to 0 and 1 how can you know what they are?

[@TMQuest]

Hi! With C1 and C2 we have a general family of solutions, with one solution for each choice of values for C1 and C2. We set C1=0 and C2=1 just to illustrate one choice of values. Without additional initial conditions on the ODE, all the solutions in the parametrized family (C1 and C2) are equally good. Hope this helps :)

[@tshepomofokeng8558]

Wow