23.2.270 problem 285

Internal problem ID [5625]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 285
Date solved : Tuesday, September 30, 2025 at 01:14:27 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.101 (sec). Leaf size: 46

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

\begin{align*} y &= -\frac {2 \sqrt {3}\, \sqrt {-a x}\, x}{9} \\ y &= \frac {2 \sqrt {3}\, \sqrt {-a x}\, x}{9} \\ y &= \frac {c_1 \left (c_1^{2}+a x \right )}{a} \\ \end{align*}

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 68

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

\begin{align*} y(x)&\to \frac {c_1{}^3}{a}+c_1 x\\ y(x)&\to -\frac {2 i \sqrt {a} x^{3/2}}{3 \sqrt {3}}\\ y(x)&\to \frac {2 i \sqrt {a} x^{3/2}}{3 \sqrt {3}} \end{align*}

✗ Sympy

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

Timed Out