89.31.12 problem 12

Internal problem ID [24957]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Exercises at page 246
Problem number : 12
Date solved : Thursday, October 02, 2025 at 11:36:36 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: 0.126 (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 &= 0 \\ y &= -\frac {2 \sqrt {-24 c_1^{3}+27 c_1 x -3 \sqrt {\left (4 c_1^{2}-3 x \right )^{3}}}}{9} \\ y &= \frac {2 \sqrt {-24 c_1^{3}+27 c_1 x -3 \sqrt {\left (4 c_1^{2}-3 x \right )^{3}}}}{9} \\ y &= -\frac {2 \sqrt {-24 c_1^{3}+27 c_1 x +3 \sqrt {\left (4 c_1^{2}-3 x \right )^{3}}}}{9} \\ y &= \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