60.1.522 problem 535

Internal problem ID [10536]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 535
Date solved : Sunday, March 30, 2025 at 05:48:35 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: 0.110 (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: 0.336 (sec). Leaf size: 77

ode=9*y[x] - 12*y[x]*D[y[x],x]^2 + 8*x*D[y[x],x]^3==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