Timeline for Riccati and Linear 1st Order ODE Parallel
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 8, 2019 at 4:11 | vote | accept | user10478 | ||
| Dec 27, 2018 at 10:40 | answer | added | JJacquelin | timeline score: 1 | |
| Dec 27, 2018 at 6:00 | comment | added | Story123 | I don't believe that every solution of a Riccati equation is given by $y= y_p + u$. In general, it is much harder to find the general solutions of a non-linear ODE. For a $n^{th}$ order linear ODEs, we know when we have a basis because there is one particular solution and $n$ linearly independent homogenous solution. But we have no such theory for non-linear ODE; there can be solutions not of the form $y= y_p + u$ and I don't see why not. I think it's just a nice trick to convert the non-linear ODE into a Bernoulli Equation, which we know how to solve. | |
| Dec 27, 2018 at 5:39 | history | asked | user10478 | CC BY-SA 4.0 |