82.8.17 problem 36-18

Internal problem ID [21888]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 36. Nonlinear differential equations. Page 1203
Problem number : 36-18
Date solved : Thursday, October 02, 2025 at 08:05:46 PM
CAS classification : [_separable]

\begin{align*} {y^{\prime }}^{2} x^{2}+4 x y y^{\prime }+3 y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=x^2*diff(y(x),x)^2+4*x*y(x)*diff(y(x),x)+3*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {c_1}{x} \\ y &= \frac {c_1}{x^{3}} \\ \end{align*}

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 26

ode=x^2*D[y[x],x]^2+4*x*y[x]*D[y[x],x]+3*y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x^3}\\ y(x)&\to \frac {c_1}{x}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x)**2 + 4*x*y(x)*Derivative(y(x), x) + 3*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {C_{1}}{x^{3}}, \ y{\left (x \right )} = \frac {C_{1}}{x}\right ] \]