89.32.9 problem 10

Internal problem ID [24969]
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. Miscellaneous Exercises at page 246
Problem number : 10
Date solved : Thursday, October 02, 2025 at 11:45:09 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} 4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.217 (sec). Leaf size: 100

ode:=4*y(x)^2*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^{{3}/{4}} 3^{{1}/{4}} x^{{3}/{4}}}{3} \\ y &= \frac {2^{{3}/{4}} 3^{{1}/{4}} x^{{3}/{4}}}{3} \\ y &= -\frac {i 2^{{3}/{4}} 3^{{1}/{4}} x^{{3}/{4}}}{3} \\ y &= \frac {i 2^{{3}/{4}} 3^{{1}/{4}} x^{{3}/{4}}}{3} \\ y &= 0 \\ y &= \sqrt {2}\, \sqrt {c_1 \left (-2 c_1^{2}+x \right )} \\ y &= -\sqrt {2}\, \sqrt {c_1 \left (-2 c_1^{2}+x \right )} \\ \end{align*}

✓ Mathematica. Time used: 92.761 (sec). Leaf size: 11250

ode=4*y[x]^2*D[y[x],x]^3-2*x*D[y[x],x]+y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*Derivative(y(x), x) + 4*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