77.23.28 problem 28

Internal problem ID [20594]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 28
Date solved : Thursday, October 02, 2025 at 06:14:58 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} 8 x {y^{\prime }}^{3}&=y \left (12 {y^{\prime }}^{2}-9\right ) \end{align*}

✓ Maple. Time used: 0.051 (sec). Leaf size: 61

ode:=8*diff(y(x),x)^3*x = y(x)*(12*diff(y(x),x)^2-9); 
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: 0.215 (sec). Leaf size: 77

ode=8*D[y[x],x]^3*x==y[x]*(12*D[y[x],x]^2-9); 
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*Derivative(y(x), x)**2 - 9)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out