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Question Number 126229 by MathSh last updated on 18/Dec/20

$$(1+y)x^{\prime }=x$$

Answered by Dwaipayan Shikari last updated on 18/Dec/20

$$(1+y)\frac{dx}{dy}=x\Rightarrow \int \frac{dy}{1+y}=\int \frac{dx}{x}\Rightarrow 1+y=Cx$$

Answered by ebi last updated on 18/Dec/20

$$(y+1)x^{\prime }=x$$$$\left(\frac{1}{x}\right)x^{\prime }=\frac{1}{y+1}$$$$\int \left(\frac{1}{x}\right)dx=\int \frac{1}{y+1}dy$$$$ln\mid x\mid =ln\mid y+1\mid +c$$$$ln\mid x\mid =ln\mid y+1\mid +ln\mid C\mid$$$$ln\mid x\mid =ln\mid C(y+1)\mid$$$$x=C(y+1)$$

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