d^2y/dx^2 – y = 2x

Question

d²y – y = 2x

dx²

 

Answer 1

d^2y/dx^2 - y = 2x

The auxiliary eqn is

m^2 - 1 = 0

m = +/- 1

The homogeneous solution is,

y1 = Ae^x + Be^(-x)

Let the 2md solution be,

y2 = Cx + D

By inspection, we can see thast C = -2, D =0. Hence

y2 = -2x

The general solution is y(x) = y1 + y2

Answer: y(x) = Ae^x + Be^(-x) - 2x