54.2.24 problem 27

Internal problem ID [8556]
Book : Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition. 1997.
Section : CHAPTER 16. Nonlinear equations. Miscellaneous Exercises. Page 340
Problem number : 27
Date solved : Monday, March 31, 2025 at 11:55:07 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: 0.142 (sec). Leaf size: 786

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: 111.655 (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