85.33.2 problem 2

Internal problem ID [22625]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 65
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:56:51 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

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

\begin{align*} y &= 0 \\ y &= -\frac {x}{2} \\ y &= -2 x \\ y &= c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to 0\\ y(x)&\to -2 x\\ y(x)&\to -\frac {x}{2}\\ y(x)&\to c_1 \end{align*}

✓ Sympy. Time used: 0.203 (sec). Leaf size: 17

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

\[ \left [ y{\left (x \right )} = - \frac {x}{2}, \ y{\left (x \right )} = - 2 x, \ y{\left (x \right )} = C_{1}\right ] \]