89.32.19 problem 22

Internal problem ID [24979]
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. Miscellaneous Exercises at page 246
Problem number : 22
Date solved : Thursday, October 02, 2025 at 11:45:17 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.184 (sec). Leaf size: 792

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 155.555 (sec). Leaf size: 15120

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

Too large to display

✗ Sympy

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

Timed Out