For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

y = x sin 3x :

It is given that y = xsin3x

Now, differentiating both sides w.r.t. x , we get,

Now, again differentiating both sides w.r.t. x, we get,

Now, substituting the value of in the LHS of the given differential equation, we get,

= (6.cos3x – 9xsin3x) + 9xsin3x – 6cos3x

= 0 = RHS

Therefore, the given function is the solution of the corresponding differential equation.