87.5.15 problem 19

Internal problem ID [23308]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 47
Problem number : 19
Date solved : Thursday, October 02, 2025 at 09:31:24 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _Bernoulli]

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

With initial conditions

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

✓ Maple. Time used: 0.048 (sec). Leaf size: 19

ode:=2*x*y(x)*diff(y(x),x)+x^2+y(x)^2 = 0; 
ic:=[y(1) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {\sqrt {-3 x \left (x^{3}-4\right )}}{3 x} \]

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 28

ode=(x^2+y[x]^2)+( 2*x*y[x] )*D[y[x],x]==0; 
ic={y[1]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\sqrt {4-x^3}}{\sqrt {3} \sqrt {x}} \end{align*}

✓ Sympy. Time used: 0.349 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 + 2*x*y(x)*Derivative(y(x), x) + y(x)**2,0) 
ics = {y(1): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {\sqrt {3} \sqrt {- x^{2} + \frac {4}{x}}}{3} \]