Find dy - dx in the following questions-2 x-3 y-sin y

Given, 2x+3y= sin y Differentiating both sides w.r.t. x, we get d/dx(2x+3y)=d/dx(sin y) ⇒ 2+3dy/dx=cos ydy/dx⇒ 3 dy/dx cos y dy/dx= 2 ⇒ (3 cos y)dy/dx= 2⇒dy ...

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Standard XII

Mathematics

Variable Separable Method

Find dy / dx ...

Question

Find $\frac{d y}{d x}$ in the following questions:

2x+3y=sin y.

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Solution

Given, 2x+3y= sin y

Differentiating both sides w.r.t. x, we get

$\frac{d}{d x} (2 x + 3 y) = \frac{d}{d x} (s i n y)$

$\Rightarrow 2 + 3 \frac{d y}{d x} = c o s y \frac{d y}{d x} \Rightarrow 3 \frac{d y}{d x} - c o s y - \frac{d y}{d x} = - 2$

$\Rightarrow (3 - c o s y) \frac{d y}{d x} = - 2 \Rightarrow \frac{d y}{d x} = \frac{2}{c o s y - 3}$

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