53.3.17 problem 20

Internal problem ID [8479]
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 : 20
Date solved : Sunday, March 30, 2025 at 01:11:37 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Maple. Time used: 0.036 (sec). Leaf size: 58

ode:=2*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}-24 x \right ) \sqrt {c_1^{2}+24 x}}{432}-\frac {c_1^{3}}{432}-\frac {c_1 x}{12} \\ y &= \frac {\left (c_1^{2}+24 x \right )^{{3}/{2}}}{432}-\frac {c_1^{3}}{432}-\frac {c_1 x}{12} \\ \end{align*}

✗ Mathematica

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

Timed out

✗ Sympy

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

Timed Out