Internal problem ID [2671]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.029 (sec). Leaf size: 33
DSolve[y[x]*(x^2-y[x]^2)-x*(x^2-y[x]^2)*y'[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*}