23.2.268 problem 283

Internal problem ID [5623]
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 : 283
Date solved : Tuesday, September 30, 2025 at 01:14:21 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Maple. Time used: 0.035 (sec). Leaf size: 442

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

\begin{align*} -\frac {c_1}{{\left (\frac {\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}+24 x}{\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{1}/{3}}}\right )}^{{2}/{3}}}+x -\frac {{\left (\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}+24 x \right )}^{2}}{96 \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}} &= 0 \\ -\frac {c_1}{{\left (\frac {i \sqrt {3}\, \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}-24 i \sqrt {3}\, x -\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}-24 x}{\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{1}/{3}}}\right )}^{{2}/{3}}}+x +\frac {3 {\left (-\frac {\left (\sqrt {3}+i\right ) \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}}{24}+x \left (-i+\sqrt {3}\right )\right )}^{2}}{2 \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}} &= 0 \\ -\frac {12^{{2}/{3}} c_1}{{\left (\frac {-i \sqrt {3}\, \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}+24 i \sqrt {3}\, x -\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}-24 x}{\left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{1}/{3}}}\right )}^{{2}/{3}}}+x +\frac {3 {\left (\frac {\left (i-\sqrt {3}\right ) \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}}{24}+\left (\sqrt {3}+i\right ) x \right )}^{2}}{2 \left (108 y+12 \sqrt {-96 x^{3}+81 y^{2}}\right )^{{2}/{3}}} &= 0 \\ \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