89.31.10 problem 10

Internal problem ID [24955]
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 : 10
Date solved : Thursday, October 02, 2025 at 11:36:34 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.182 (sec). Leaf size: 167

ode:=y(x)^4*diff(y(x),x)^3-6*x*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {\left (-i \sqrt {3}-1\right ) x} \\ y &= \sqrt {x \left (i \sqrt {3}-1\right )} \\ y &= -\sqrt {-x \left (1+i \sqrt {3}\right )} \\ y &= -\sqrt {x \left (i \sqrt {3}-1\right )} \\ y &= \sqrt {2}\, \sqrt {x} \\ y &= -\sqrt {2}\, \sqrt {x} \\ y &= 0 \\ y &= \frac {2^{{2}/{3}} \left (-c_1^{3}+6 c_1 x \right )^{{1}/{3}}}{2} \\ y &= -\frac {2^{{2}/{3}} \left (-c_1^{3}+6 c_1 x \right )^{{1}/{3}} \left (1+i \sqrt {3}\right )}{4} \\ y &= \frac {2^{{2}/{3}} \left (-c_1^{3}+6 c_1 x \right )^{{1}/{3}} \left (i \sqrt {3}-1\right )}{4} \\ \end{align*}

✓ Mathematica. Time used: 46.683 (sec). Leaf size: 22649

ode=y[x]^4*D[y[x],x]^3-6*x*D[y[x],x]+2*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(-6*x*Derivative(y(x), x) + y(x)**4*Derivative(y(x), x)**3 + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out