84.10.9 problem 5.19

Internal problem ID [22137]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 5. Homogeneous differential equations. Supplementary problems
Problem number : 5.19
Date solved : Thursday, October 02, 2025 at 08:31:30 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 64

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

\begin{align*} y &= -\frac {\sqrt {2}\, \sqrt {-2 \left (\ln \left (x \right )+c_1 +\frac {1}{2}\right ) \left (c_1 +\ln \left (x \right )\right )}\, x}{2 c_1 +2 \ln \left (x \right )} \\ y &= \frac {\sqrt {2}\, \sqrt {-2 \left (\ln \left (x \right )+c_1 +\frac {1}{2}\right ) \left (c_1 +\ln \left (x \right )\right )}\, x}{2 c_1 +2 \ln \left (x \right )} \\ \end{align*}

✓ Mathematica. Time used: 0.177 (sec). Leaf size: 86

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

\begin{align*} y(x)&\to -\frac {x \sqrt {2 \log (x)+1+2 c_1}}{\sqrt {-2 \log (x)-2 c_1}}\\ y(x)&\to \frac {x \sqrt {2 \log (x)+1+2 c_1}}{\sqrt {-2 \log (x)-2 c_1}}\\ y(x)&\to -i x\\ y(x)&\to i x \end{align*}

✗ Sympy

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

RecursionError : maximum recursion depth exceeded