What will be general solution of differential equation d²y/dx² = e^2x(12 cos3x – 5 sin3x)? (here, A and B are integration constant)

Given, d²y/dx² = e^2x(12 cos3x ? 5 sin3x) ???(1)
Integrating (1) we get,
dy/dx = 12∫ e^2xcos3x dx – 5∫ e^2x sin3x dx
= 12 * (e^2x/2² + 3²)[2cos3x + 3sin3x] ? 5 * (e^2x/2² + 3²)[2sin3x ? 3cos3x] + A (A is integrationconstant)
So dy/dx = e^2x/13 [24 cos3x + 36 sin3x ? 10 sin3x + 15 cos3x] + A
= e^2x/13(39 cos3x + 26 sin3x) + A
=> dy/dx = e^2x(3 cos3x + 2 sin3x) + A ???.(2)
Again integrating (2) we get,
y = 3*∫ e^2x cos3xdx + 2∫ e^2x sin3xdx + A ∫dx
y = 3*(e^2x/2² + 3²)[2cos3x + 3sin3x] + 2*(e^2x/2² + 3²)[2sin3x ? 3cos3x] + Ax + B (B is integration constant)
y = e^2x/13(6 cos3x + 9 sin3x + 4 sin3x ? 6 cos3x) + Ax + B
or, y = e^2x sin3x + Ax + B