Order linear nonhomogeneous ODEs

Question

Solving nth order linear nonhomogeneous ODEs the method of undetermined coefficients what can be used to find a particular solution of the ODE(s)?

A.) y''-y=tanh(x)

B.)y''-y=cot x

C.) y''(x)-y(x)=cosh(x)

D.) y''(x)-y(x)=(sinx)^2

Answer 1

I think that we can use method of undetermined coefficients only for C) and D), becose: side is

C) rightright side is cosh(x) = (e^x + e^-x)/2 and roots of characteristic equation are 1 and -1 so y_p= axe^x + bxe^-x

D) right side is sin²x = 1/2 - 1/2cos2x, So we can look for y_p = a + bsin2x + ccos2x