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  • Verify that the given function (implicit or explicit) is a solution of the corresponding differential equation. (iii) y = x sin 3x

Q2.    Verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

            (iii)    y= x\sin 3x \qquad : \ \frac{d^2y}{dx^2} + 9y - 6\cos 3x = 0

 

Answers (1)

best_answer

Given,

y= x\sin 3x

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

y= x\sin 3x \frac{dy}{dx} = x(3\cos 3x) + \sin 3x

Again, differentiating both sides w.r.t. x,

\\ \frac{d^2y}{dx^2} = 3x(-3\sin 3x) + 3\cos 3x + 3\cos 3x \\ = -9y + 6\cos 3x \\ \implies \frac{d^2y}{dx^2} + 9y - 6\cos 3x = 0

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

Posted by

HARSH KANKARIA

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