66.1.48 problem Problem 62

Internal problem ID [13895]
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 62
Date solved : Tuesday, January 28, 2025 at 06:07:47 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.083 (sec). Leaf size: 47

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

\begin{align*} y &= \frac {1-\sqrt {-4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ y &= \frac {1+\sqrt {-4 c_{1}^{2} x^{2}+1}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.926 (sec). Leaf size: 66

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

\begin{align*} y(x)\to \frac {1}{2} \left (e^{c_1}-\sqrt {-4 x^2+e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {-4 x^2+e^{2 c_1}}+e^{c_1}\right ) \\ y(x)\to 0 \\ \end{align*}