Question

Show that, for the differential equation d^2y/dx^2 + a(x)dy/dX + b(x)y=0, e^(mx) is a particular integral if m^2+am+b=0. Hence find the value of m so that e^(mx) is a particular integral of the equation (x-2)d^2y/dx^2-(4x-7)dy/dX + (4x-6)y=0.