84.14.8 problem 7.16

Internal problem ID [22165]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 7. Integrating factors. Supplementary problems
Problem number : 7.16
Date solved : Thursday, October 02, 2025 at 08:33:10 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 31

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

\begin{align*} y &= 0 \\ y &= \sqrt {-2 x^{2}+c_1} \\ y &= -\sqrt {-2 x^{2}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 56

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

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

✓ Sympy. Time used: 0.376 (sec). Leaf size: 29

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

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} - 2 x^{2}}, \ y{\left (x \right )} = \sqrt {C_{1} - 2 x^{2}}, \ y{\left (x \right )} = 0\right ] \]