89.30.3 problem 5

Internal problem ID [24920]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Exercises at page 243
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:49:44 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} 2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \end{align*}

✓ Maple. Time used: 0.274 (sec). Leaf size: 56

ode:=2*x*diff(y(x),x)^3-6*y(x)*diff(y(x),x)^2+x^4 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {\left (1+i \sqrt {3}\right ) x^{2}}{4} \\ y &= \frac {\left (i \sqrt {3}-1\right ) x^{2}}{4} \\ y &= \frac {x^{2}}{2} \\ y &= \frac {1}{6 c_1^{2}}+\frac {c_1 \,x^{3}}{3} \\ \end{align*}

✓ Mathematica. Time used: 175.61 (sec). Leaf size: 21360

ode=2*x*D[y[x],x]^3-6*y[x]*D[y[x],x]^2+x^4==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**4 + 2*x*Derivative(y(x), x)**3 - 6*y(x)*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out