1.11 problem 11

Internal problem ID [4971]

Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number: 11.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {y^{\prime }-y^{2} x -2 y x=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 19

dsolve(diff(y(x),x)-x*y(x)^2=2*x*y(x),y(x), singsol=all)
 

\[ y \relax (x ) = \frac {2}{-1+2 \,{\mathrm e}^{-x^{2}} c_{1}} \]

Solution by Mathematica

Time used: 0.42 (sec). Leaf size: 31

DSolve[y'[x]-2*x*y[x]^2==2*x*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -1+\frac {1}{1-e^{x^2+c_1}} \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}