Here's the second one
For the homogeneous solution, try , thus we get the characteristic equation:
For a particular solution, try ........I hope you notice your mistake here. You reused A and B for the sine and cosine functions, you can't do that, they should be different variables!
Plug these into the original equation, we get:
Collect like terms:
Equating coefficients we get:
Thus the general solution is: