Verify that the function y = 4 sin 3x is a solution of the differentia

1.	Verify that the function y = 4 sin 3x is a solution of the differential equation d2y/dx2 + 9y = 0.
Answer» The given function is y = 4 sin 3x Differentiating both sides with respect to x, we have img 177 Again, differentiating both sides with respect to x, we have img 18 Putting values of d²y/dx² and y in the given differential equation, we have L.H.S. = – 36 sin 3x + 9 (4 sin 3x) = – 36 sin 3x + 36 sin 3x = 0 = R.H.S. Thus, y = 4 sin 3x is a solution of differential equation img 20.

Verify that the function y = 4 sin 3x is a solution of the differential equation d2y/dx2 + 9y = 0.

Answer»

The given function is y = 4 sin 3x

Differentiating both sides with respect to x, we have

img 177

Again, differentiating both sides with respect to x, we have

img 18

Putting values of d²y/dx² and y in the given differential equation, we have

L.H.S. = – 36 sin 3x + 9 (4 sin 3x) = – 36 sin 3x + 36

sin 3x = 0 = R.H.S.

Thus, y = 4 sin 3x is a solution of differential equation img 20.