Mathematics - Differential Equation Question with Solution | TestHub

$x^2=e^{{\left(\frac{x}{y}\right)}^{-1}\left(\frac{dy}{dx}\right)}\Rightarrow x^2=e^{\left(\frac{y}{x}\right)\left(\frac{dy}{dx}\right)}$ $\Rightarrow \ln x^2=\frac{y}{x}\frac{dy}{dx}$ or $\int x\ln x^{2}dx=\int ydy$ Put $x^2=t\Rightarrow 2xdx=dt\therefore \frac{1}{2}\int \ln tdt=\frac{y^2}{2}$ $C+t\ln t-t=y^2$ or $y^2=x^2\left(\ln x^2-1\right)+C$