47.2.9 problem 16

Internal problem ID [9748]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 97. The p-discriminant equation. EXERCISES Page 314
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 06:32:46 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: 0.204 (sec). Leaf size: 161

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: 34.681 (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