20.4.7 problem Problem 15

Internal problem ID [3642]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 15
Date solved : Monday, January 27, 2025 at 07:49:30 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 17

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

\begin{align*} y \left (x \right ) &= -x \\ y \left (x \right ) &= x \\ y \left (x \right ) &= c_{1} x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 33

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

\begin{align*} y(x)\to -x \\ y(x)\to x \\ y(x)\to c_1 x \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}