d2y/dx2+9y=cos2x+sin2x

Answer 1

y" + 9y = cos2x+sin2x

You know that

y"+9y=0
has solutions
y = a cos3x + b sin3x

so the solution here is

y = a cos 3x + b sin 3x + (cos2x+sin2x)/5

Answer 2

y+9y=3x+e^x