53.3.26 problem 29

Internal problem ID [8488]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 99. Clairaut equation. EXERCISES Page 320
Problem number : 29
Date solved : Wednesday, March 05, 2025 at 06:01:05 AM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 105.496 (sec). Leaf size: 7052

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

Timed Out