1. The problem statement, all variables and given/known data Why do we need two solutions to solve a 2nd order linear differential equation? lets consider a differential equation with equal roots for auxiliary equation. So the reasoning behind why cant we use y=Aen1x+Ben2x as its general solution is because since the roots are equal we get a single solution y=Cenx . So my question is what's the problem with having one solution? After all it's A SOLUTION.