66.1.11 problem Problem 11

Internal problem ID [13858]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 1, First-Order Differential Equations. Problems page 88
Problem number : Problem 11
Date solved : Tuesday, January 28, 2025 at 06:05:37 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.108 (sec). Leaf size: 55

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

\begin{align*} y(x)\to c_1 x \\ y(x)\to -\sqrt {x^2+2 c_1} \\ y(x)\to \sqrt {x^2+2 c_1} \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}