47.2.2 problem 2

Internal problem ID [7418]
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
Date solved : Monday, January 27, 2025 at 02:53:45 PM
CAS classification : [_separable]

\begin{align*} y-2 y x +x^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

dsolve((y(x)-2*x*y(x))+x^2*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 23

DSolve[(y[x]-2*x*y[x])+x^2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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