Answer to Question #195907 in Differential Equations for Anuradha Singh jad

Question

Solve the following equation of first order but not of first degree y=2xp-p²

Answer 1

$\text{Given, the equation} y=2xp-p².\newline \text{Differentiate wrt} x.\newline p=2p-2pr\newline \text{where}p=\frac{dy}{dx} \text{and }\frac{dp}{dx}.\newline 1=2-2r\newline r=\frac{1}{2}\newline \frac{dp}{dx}=\frac{1}{2}\newline dp=\frac{1}{2}dx\newline \text{Integrate wrt}x,\newline p=\frac{x}{2}+C\newline \frac{dy}{dx}=\frac{x}{2}+C\newline dy=(\frac{x}{2}+C)dx\newline \text{Integrate wrt} x,\newline y=\frac{x^2}{4}+Cx+D$