53.3.21 problem 24

Internal problem ID [8483]
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 : 24
Date solved : Sunday, March 30, 2025 at 01:11:43 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 58

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

\begin{align*} y &= \frac {\left (c_1^{2}-12 x \right )^{{3}/{2}}}{108}-\frac {c_1^{3}}{108}+\frac {c_1 x}{6} \\ y &= \frac {\left (-c_1^{2}+12 x \right ) \sqrt {c_1^{2}-12 x}}{108}-\frac {c_1^{3}}{108}+\frac {c_1 x}{6} \\ \end{align*}

✓ Mathematica. Time used: 158.124 (sec). Leaf size: 10134

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

Timed Out