suppose we have second order ODE, that is $y''+ p(x)y'+ q(x)y = 0 $. Then let $y_1$ and $y_2$ be solutions of this ODE. Its obvious that $c_1y_1 +c_2y_2$ will also be solution, where we call this form general solution.
Now my questions are:
Why do we need general solution if $y_n$ alone satisfies the ODE?
Is the concept of general solution consequence of initial value problem?