23.2.315 problem 340

Internal problem ID [5670]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 340
Date solved : Tuesday, September 30, 2025 at 01:48:55 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: 0.297 (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: 65.02 (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