By using the substitution $u=xe^{y}$, find $y$ in terms of $x$ given that \(e^{y}\left(x\frac{

Question

By using the substitution $u=xe^{y}$, find $y$ in terms of $x$ given that $e^{y}\left(x\frac{\mathrm{d}y}{\mathrm{d}x}+1\right)=2x$, and that $y=0$ when $x=2$.

Accepted Answer

$y=\ln\left(\frac{x^2-2}{x}\right),\ x>\sqrt{2}$

Differential Equations - Solving Differential Equations by Substitution

Differential Equations - Solving Differential Equations by Substitution

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