Browse Questions

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

$y=x\;\sin 3x$ $\:$:$\:$ $\frac{d^2y}{dx^2}+9y-6\;\cos 3x=0$

Toolbox:
• $\large\frac{d(e^x)}{dx }$$= e^x; \large\frac{d(x)}{dx}$$ = 1$; $\large\frac{d(constant\; term )} {dx}= $$0. The product rule of differentiation states uv = uv' + vu' Step 1: Given y = x\sin 3x Differentiating on both sides we get, \large\frac{dy}{dx}$$= x. (3\cos3x) + (\sin3x).1$
$\large\frac{dy}{dx} $$= 3x\cos 3x + \sin 3x differentiating again we get \large\frac{d^2y}{dx^2 }$$= 3x.(- 3\sin 3x) + 3x(\cos 3x) + (3\cos 3x)$

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