I´m trying to learn to use the Euler method to solve a system of ODE's. I understand pretty clearly how to apply it when I have a single equation. But I stumbled uppon the following system which claims can be solved using Euler method: \begin{cases} x' +y' = 4t\\ -x' +y' +y = 6t^2 +10 \end{cases} Can anyone explain me how can I use the Euler method on this kind of systems?

Thank you!

  • 1
    $\begingroup$ Maybe try $u=x+y, v=-x+y$ and express $x,y$ in terms of $u,v$. $\endgroup$ – copper.hat May 20 '17 at 6:13
  • $\begingroup$ Or add and subtract both equations to find the explicit form of the system. $\endgroup$ – LutzL May 20 '17 at 6:14
  • $\begingroup$ Is the explicit form of the system getting 2 equations of the form $x'=f(t,y) $and $y'=f(t,y)$ ? $\endgroup$ – Pablo Estrada May 20 '17 at 6:17
  • $\begingroup$ @PabloEstrada: Essentially yes, but different $f$s for $x,y$. $\endgroup$ – copper.hat May 20 '17 at 6:17
  • $\begingroup$ Ok thank you very much :) $\endgroup$ – Pablo Estrada May 20 '17 at 6:18

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