47.2.25 problem 25

Internal problem ID [7441]
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 : 25
Date solved : Monday, January 27, 2025 at 02:59:39 PM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x)^2-3*x*y(x)*diff(y(x),x)+2*y(x)^2=0,y(x), singsol=all)
 

\begin{align*} y &= c_{1} x^{2} \\ y &= c_{1} x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 24

DSolve[x^2*(D[y[x],x])^2-3*x*y[x]*D[y[x],x]+2*y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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