29.35.5 problem 1037

Internal problem ID [5603]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 35
Problem number : 1037
Date solved : Sunday, March 30, 2025 at 09:07:46 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} {y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \end{align*}

✓ Maple. Time used: 0.362 (sec). Leaf size: 47

ode:=diff(y(x),x)^3-x*y(x)^4*diff(y(x),x)-y(x)^5 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {3 \sqrt {3}}{2 x^{{3}/{2}}} \\ y &= \frac {3 \sqrt {3}}{2 x^{{3}/{2}}} \\ y &= 0 \\ y &= c_1 \sqrt {\frac {c_1^{10}}{\left (c_1^{4} x -1\right )^{2}}} \\ \end{align*}

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 64

ode=(D[y[x],x])^3 -x*y[x]^4*D[y[x],x]- y[x]^5==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{c_1 x-c_1{}^3} \\ y(x)\to 0 \\ y(x)\to \text {Indeterminate} \\ y(x)\to -\frac {3 \sqrt {3}}{2 x^{3/2}} \\ y(x)\to \frac {3 \sqrt {3}}{2 x^{3/2}} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*y(x)**4*Derivative(y(x), x) - y(x)**5 + Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out