29.34.25 problem 1027

Internal problem ID [5596]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 34
Problem number : 1027
Date solved : Sunday, March 30, 2025 at 09:05:36 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 141

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

\begin{align*} y &= \frac {2 \left (\sqrt {x^{2}+3 c_1}-2 x \right ) \sqrt {-6 \sqrt {x^{2}+3 c_1}-6 x}}{9} \\ y &= -\frac {2 \left (\sqrt {x^{2}+3 c_1}-2 x \right ) \sqrt {-6 \sqrt {x^{2}+3 c_1}-6 x}}{9} \\ y &= -\frac {2 \left (\sqrt {x^{2}+3 c_1}+2 x \right ) \sqrt {6 \sqrt {x^{2}+3 c_1}-6 x}}{9} \\ y &= \frac {2 \left (\sqrt {x^{2}+3 c_1}+2 x \right ) \sqrt {6 \sqrt {x^{2}+3 c_1}-6 x}}{9} \\ \end{align*}

✗ Mathematica

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

Timed Out