ok im trying to solve the following equation using standard aux method: d^2y/dx^2 + 3dy/dy +2y = cos x with conditions x(0)=-3 and x'(0) = 3 my aux eqn is: ae^x + be^-2x and my yp is; a sin kx + b cos kx i differentiate this twice and substitute into the original equation, and i get: (-a sin x - b cos x)+3(a cos x-b sin x) + 2(a sin x+ b cos x) = cos x. Now at this stage im not sure if this is right or not, can someone please confirm if this is right or not. I ve done this question using the laplace method and the answer i get is; -19/2e^x +32/5 e^2x + 1/10 cos x - 3/10 sin x. Here my aux equation is not the same as what i get when i apply the laplace method. Im not sure what is going wrong. Someone help me please.