Find the general solution of the second order differential equation: y''+2y'-3 = 0

This is a homogeneous second order equation with constant coefficients, so all we need to do is find the complementary function: We write: m²+2m-3=0 which has solutions m=1 or m=-3 We have two real solutions, so we get two exponential terms in the general solution: e^x and e^-3x This gives the general solution (putting in arbitrary constants): y = Ae^x+Be^-3x