Timeline for Transform expression into a certain standard form for an ODE
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 9, 2019 at 1:19 | history | edited | Michael E2 |
edited tags
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| Mar 9, 2019 at 0:59 | answer | added | Michael E2 | timeline score: 1 | |
| Mar 8, 2019 at 0:07 | comment | added | Michael E2 |
The term linear applied to ODE usually means the equation is linear in the "dependent variables" $y(x)$ and its derivatives, that is, an equation of the form $\sum a_k(x) y^{(k)}(x) = p(x)$; the coefficients $a_k(x)$ and $p(x)$ may be any functions of $x$. Nonlinear equations have dependent variables in nonlinear functions such as $\sin(y(x))$ or x''[z]^2. It seems you are considering only the special case of linear ODES with constant coefficients, not any given ODE such as the one in my comment. That's fine; I just wanted to know since the accepted answer deals only with this special case.
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| Mar 7, 2019 at 21:57 | history | edited | Taylor Raine | CC BY-SA 4.0 |
added 9 characters in body
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| Mar 7, 2019 at 21:57 | comment | added | Taylor Raine | @MichaelE2, I have added some clarifications to the question, but generally, if the ODE is non-linear, then the non-linear aspect of the equation should be moved to the RHS of the expression. | |
| Mar 7, 2019 at 21:49 | history | edited | Taylor Raine | CC BY-SA 4.0 |
Clarifications
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| Mar 7, 2019 at 21:45 | comment | added | Michael E2 | What would be the desired form in that case, given that it's nonlinear? | |
| Mar 7, 2019 at 21:38 | comment | added | Taylor Raine | @MichaelE2, no, that does not present the format that I am looking for | |
| Mar 7, 2019 at 21:35 | vote | accept | Taylor Raine | ||
| Mar 2, 2019 at 0:42 | comment | added | Michael E2 |
Generalized, including nonlinear equations? E.g. Apply[Equal, Solve[a x'[z] == -b x[z] + c x''[z]^2, {x''[z]}], {2}] -- is it how you'd like?
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| Mar 2, 2019 at 0:24 | history | edited | m_goldberg | CC BY-SA 4.0 |
Routine cleanup
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| Mar 1, 2019 at 17:20 | answer | added | march | timeline score: 4 | |
| Mar 1, 2019 at 16:40 | review | First posts | |||
| Mar 2, 2019 at 0:24 | |||||
| Mar 1, 2019 at 16:38 | history | asked | Taylor Raine | CC BY-SA 4.0 |