Find d y d x if 2x + 3y = sin x - Vidyadip

Question

Find $\frac{d y}{d x}$ if 2x + 3y = sin x

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Answer

It is given that 2x + 3y = sin x
Differentiating both sides w.r.t. x, we get,
$\frac{d}{d x}(2 x)+\frac{d}{d x}(3 y)=\frac{d}{d x}(\sin x)$
$\Rightarrow 2+3 \frac{d y}{d x}$ = cos x
$\Rightarrow$ $3 \frac{d y}{d x}=\cos x-2$
$\Rightarrow \frac{d y}{d x}=\frac{\cos x-2}{3}$

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