(dy/dx) = (1/(3e^y −2x)) ?


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Question Number 105238 by bemath last updated on 27/Jul/20

$\frac{d y}{d x} = \frac{1}{3 e^{y} - 2 x} ?$
	Answered by john santu last updated on 27/Jul/20

	$\frac{d x}{d y} = 3 e^{y} - 2 x$ $\frac{d x}{d y} + 2 x = 3 e^{y}$ $i n t e g r a t i n g f a c t o r$ $u (y) = e^{\int 2 d y} = e^{2 y}$ $\Leftrightarrow e^{2 y} \frac{d x}{d y} + 2 {x e}^{2 y} = 3 e^{3 y}$ $\frac{d}{d y} [x . e^{2 y}] = 3 e^{3 y}$ $\int \frac{d}{d y} [x . e^{2 y}] d y = \int 3 e^{3 y} d y$ $x . e^{2 y} = e^{3 y} + C$ $∴ x = e^{y} + {C e}^{- 3 y}$ $(J S ♠ ⧫)$
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