23.2.289 problem 308

Internal problem ID [5644]
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 : 308
Date solved : Tuesday, September 30, 2025 at 01:24:02 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} 2 {y^{\prime }}^{3}+x y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 58

ode:=2*diff(y(x),x)^3+x*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\left (-c_1^{2}-24 x \right ) \sqrt {c_1^{2}+24 x}}{432}-\frac {c_1^{3}}{432}-\frac {c_1 x}{12} \\ y &= \frac {\left (c_1^{2}+24 x \right )^{{3}/{2}}}{432}-\frac {c_1^{3}}{432}-\frac {c_1 x}{12} \\ \end{align*}

✗ Mathematica

ode=2 (D[y[x],x])^3 +x D[y[x],x]-2 y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

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

Timed Out