How to Solve the Differential Equation x'' - x = t sin(t)?

[rbailey5]

Homework Statement

x(t)^double prime-x(t)=tsint

Homework Equations

The Attempt at a Solution

in this case would I start this as x=t(A(2)+A(1))sint or do i also have to use the cos which makes it
x=t(A(2)+A(1))sint+t(B(2)+B(1))cost?

 

[ehild]

See attachment.

ehild