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Question Number 108047 by bemath last updated on 14/Aug/20

$$\frac{°\bullet \mathcal{B}e\mathcal{M}ath\bullet °}{\mathrm{\Sigma }}$$$$y-x\frac{dy}{dx}=a(1+x^2\frac{dy}{dx})$$

Answered by john santu last updated on 14/Aug/20

$$\frac{\mathrm{♢}\mathcal{JS}★}{✓}$$$$\Rightarrow y-a=({ax}^2+x)\frac{dy}{dx}$$$$\Rightarrow \frac{dx}{ax(1+x)}=\frac{dy}{y-a}$$$$\Rightarrow \frac{1+x-x}{x(1+x)}dx=\frac{ady}{y-a}$$$$\int \frac{dx}{x}-\int \frac{dx}{1+x}=\int \frac{ady}{y-a}$$$$\Rightarrow \ln \mid \frac{x}{1+x}\mid +c=a\ln \mid y-a\mid$$$$\Rightarrow {(y-a)}^a=\frac{Cx}{1+x}.$$

Commented by bemath last updated on 14/Aug/20

$$coollnice$$

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