47.1.11 problem 11

Internal problem ID [7392]
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
Date solved : Monday, January 27, 2025 at 02:51:53 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }-x y^{2}&=2 y x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.395 (sec). Leaf size: 37

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

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