23.2.299 problem 319

Internal problem ID [5654]
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 : 319
Date solved : Tuesday, September 30, 2025 at 01:24:11 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} 8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \end{align*}

✓ Maple. Time used: 0.056 (sec). Leaf size: 61

ode:=8*x*diff(y(x),x)^3-12*y(x)*diff(y(x),x)^2+9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {3 x}{2} \\ y &= \frac {3 x}{2} \\ y &= 0 \\ y &= -\frac {\left (3 c_1 +x \right ) \sqrt {c_1 \left (3 c_1 +x \right )}}{3 c_1} \\ y &= \frac {\left (3 c_1 +x \right ) \sqrt {c_1 \left (3 c_1 +x \right )}}{3 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.196 (sec). Leaf size: 77

ode=8 x (D[y[x],x])^3 -12 y[x] (D[y[x],x])^2 + 9 y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {(x+3 c_1){}^{3/2}}{3 \sqrt {c_1}}\\ y(x)&\to \frac {(x+3 c_1){}^{3/2}}{3 \sqrt {c_1}}\\ y(x)&\to 0\\ y(x)&\to \text {Indeterminate}\\ y(x)&\to -\frac {3 x}{2}\\ y(x)&\to \frac {3 x}{2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(8*x*Derivative(y(x), x)**3 - 12*y(x)*Derivative(y(x), x)**2 + 9*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out