89.30.14 problem 16

Internal problem ID [24931]
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 : 16
Date solved : Saturday, October 04, 2025 at 05:36:08 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} {y^{\prime }}^{4} x -2 y {y^{\prime }}^{3}+12 x^{3}&=0 \end{align*}

✓ Maple. Time used: 0.161 (sec). Leaf size: 66

ode:=x*diff(y(x),x)^4-2*y(x)*diff(y(x),x)^3+12*x^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {2 \sqrt {6}\, \left (-x \right )^{{3}/{2}}}{3} \\ y &= -\frac {2 \sqrt {6}\, \left (-x \right )^{{3}/{2}}}{3} \\ y &= -\frac {2 \sqrt {6}\, x^{{3}/{2}}}{3} \\ y &= \frac {2 \sqrt {6}\, x^{{3}/{2}}}{3} \\ y &= \frac {12 c_1^{4}+x^{2}}{2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 27.06 (sec). Leaf size: 30947

ode=x*D[y[x],x]^4-2*y[x]*D[y[x],x]^3+12*x^3==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(12*x**3 + x*Derivative(y(x), x)**4 - 2*y(x)*Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out