# Differential Equation System With The Euler Method

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!

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