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 : Sunday, March 30, 2025 at 01:57:37 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*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\begin{align*} y &= -x \\ y &= x \\ y &= c_1 x \\ \end{align*}

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

ode=y[x]*(x^2-y[x]^2)-x*(x^2-y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.297 (sec). Leaf size: 5

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(x**2 - y(x)**2)*Derivative(y(x), x) + (x**2 - y(x)**2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x \]