Internal problem ID [4997]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y-2 y x +y^{\prime } x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve((y(x)-2*x*y(x))+x^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {1}{x}} x^{2} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 21
DSolve[(y[x]-2*x*y[x])+x^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{\frac {1}{x}} x^2 \\ y(x)\to 0 \\ \end{align*}