29.36.11 problem 1077

Internal problem ID [5638]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1077
Date solved : Tuesday, March 04, 2025 at 10:57:43 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.187 (sec). Leaf size: 133

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

\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= -\frac {2 \sqrt {-24 c_{1}^{3}+27 c_{1} x -3 \sqrt {\left (4 c_{1}^{2}-3 x \right )^{3}}}}{9} \\ y \left (x \right ) &= \frac {2 \sqrt {-24 c_{1}^{3}+27 c_{1} x -3 \sqrt {\left (4 c_{1}^{2}-3 x \right )^{3}}}}{9} \\ y \left (x \right ) &= -\frac {2 \sqrt {-24 c_{1}^{3}+27 c_{1} x +3 \sqrt {\left (4 c_{1}^{2}-3 x \right )^{3}}}}{9} \\ y \left (x \right ) &= \frac {2 \sqrt {-24 c_{1}^{3}+27 c_{1} x +3 \sqrt {\left (4 c_{1}^{2}-3 x \right )^{3}}}}{9} \\ \end{align*}

✗ Mathematica

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

IndexError : list index out of range