81.3.10 problem 4-15

Internal problem ID [21509]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 4. Homogeneous differential equations.
Problem number : 4-15
Date solved : Thursday, October 02, 2025 at 07:44:36 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} x^{2}-3 y^{2}+2 x y y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=x^2-3*y(x)^2+2*x*y(x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {c_1 x +1}\, x \\ y &= -\sqrt {c_1 x +1}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.166 (sec). Leaf size: 34

ode=(x^2-3*y[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 -x \sqrt {1+c_1 x}\\ y(x)&\to x \sqrt {1+c_1 x} \end{align*}

✓ Sympy. Time used: 0.233 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2 + 2*x*y(x)*Derivative(y(x), x) - 3*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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