82.23.8 problem Ex. 9

Internal problem ID [18785]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IV. Singular solutions. problems on chapter IV. page 49
Problem number : Ex. 9
Date solved : Thursday, March 13, 2025 at 12:56:13 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} \left (8 {y^{\prime }}^{3}-27\right ) x&=12 {y^{\prime }}^{2} y \end{align*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 86

ode:=(8*diff(y(x),x)^3-27)*x = 12*y(x)*diff(y(x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y \left (x \right ) &= -\frac {3 \,2^{{1}/{3}} x}{2} \\ y \left (x \right ) &= -\frac {3 \,2^{{1}/{3}} \left (i \sqrt {3}-1\right ) x}{4} \\ y \left (x \right ) &= \frac {3 \,2^{{1}/{3}} \left (1+i \sqrt {3}\right ) x}{4} \\ y \left (x \right ) &= \frac {8 x \sqrt {c_{1} x}-27 c_{1}^{2}}{12 c_{1}} \\ y \left (x \right ) &= \frac {-27 c_{1}^{2}-8 x \sqrt {c_{1} x}}{12 c_{1}} \\ \end{align*}

✓ Mathematica. Time used: 39.527 (sec). Leaf size: 15103

ode=(8*D[y[x],x]^3-27)*x==12*D[y[x],x]^2*y[x]; 
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*(8*Derivative(y(x), x)**3 - 27) - 12*y(x)*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out