23.2.293 problem 312

Internal problem ID [5648]
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 : 312
Date solved : Tuesday, September 30, 2025 at 01:24:06 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.035 (sec). Leaf size: 43

ode:=8*diff(y(x),x)^3+12*diff(y(x),x)^2 = 27*x+27*y(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(x+y[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