The differential equation is and the function that is to be proven as the solution is

y = 4 sin 3x, now we need to find .

12 cos 3x

– 36 sin 3x

Putting the values in the equation, we get,

–36 sin 3x + 9(4 sin 3x) = 0,

0 = 0

As, L.H.S = R.H.S. the equation is satisfied, so hence this function is the solution of the differential equation.