How to solve a coupled differential equations I tried different ways to solve this differential equation but I did not succeed. These is the first couple ODEs I try to solve. I hope somebody can give me a hint.
\begin{eqnarray}
\ddot{x} + ax - b\dot{y} = c
\end{eqnarray}
\begin{eqnarray}
\ddot{y} + ay + b\dot{x} = 0
\end{eqnarray}

$$x''+ax−by'=c \rightarrow (x''+ax−by'=c )'\rightarrow x'''+ax'-by''=0 \\y''+ay+bx'=0 \rightarrow x'=-\frac{y''+ay}{b} \rightarrow x''=-\frac{y'''+ay'}{b} $$ now put x',x'' into 1st equation 
you will have 
$$-\frac{y'''+ay'}{b}+ay-b\frac{y''+ay}{b}=0 $$
