I have this problem:
solve this ODE
so the Characteristic Equation is going to be:
i'm going to get a complex root correct? I'm really unsure on how to approach complex roots.
A function differentiated twice gives the negative of the same function, so it can be either A*cosine(bx) or B*sine(bx). By principle of superposition of the results (which is saying if two solutions are there bundle them up together)... u(x)=A cos (bx) + B sin (bx)