I am trying to solve the following coupled differential equations, \begin{align} f''(x)+c_1(f(x)+g(x))&=0\\ g''(x)+c_2(f(x)+g(x))&=0 \end{align}
where $c_1$ and $c_2$ are positive constants. The problem is I don't know any boundary conditions. The only condition that I can think of is $f(\infty)=g(\infty)=0$. How can I solve this?