Internal problem ID [4970]
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]
\[ \boxed {y^{\prime }-x y^{2}-2 x y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x)-x*y(x)^2=2*x*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {2}{-1+2 c_{1} {\mathrm e}^{-x^{2}}} \]
✓ Solution by Mathematica
Time used: 0.266 (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*}