Hey, guys. I'm having trouble finding the general solution to a second order, homogeneous ODE. It is the first step to solving an eigenvalue problem and my professor is about as much help as a hole in the head. I've tried multiple "guesses" and have combed various resources looking for general solutions and have come up empty. Can someone help out, please?
X''(x) + X'(x) - λX(x) = 0
X(0) = 0, X(a) = 0
The Attempt at a Solution
I cannot even solve the characteristic equation, m^2 + m - λ = 0 because you end up getting √1+4λ under the radical in the quadratic equation. In summary, I'm stuck, haha.