69.11.8 problem 267

Internal problem ID [18146]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 11. Singular solutions of differential equations. Exercises page 92
Problem number : 267
Date solved : Thursday, October 02, 2025 at 03:02:07 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.030 (sec). Leaf size: 37

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

\begin{align*} y &= x -\frac {4}{27} \\ y &= \left (c_1 -x \right ) \sqrt {-c_1 +x}+c_1 \\ y &= \left (-c_1 +x \right )^{{3}/{2}}+c_1 \\ \end{align*}

✗ Mathematica

ode=8*D[y[x],x]^3-12*D[y[x],x]^2==27*(y[x]-x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(27*x - 27*y(x) + 8*Derivative(y(x), x)**3 - 12*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out