Question

Please help! Find two independent real solutions of the homogeneous d.e., to the following inhomogeneous Sturm-Liouville problem:

Answer 1

\[L(y)=(e^{3x}y')'=f(x), 0 \le x <2\]\[y(0)-y'(0)=0=y'(2)\]

Answer 2

This eventually leads to finding the Green's function to the problem... So there may be some follow up questions to this! Cheers in advance :)