78.1.24 problem 2 (j)

Internal problem ID [18008]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (j)
Date solved : Monday, March 31, 2025 at 04:56:18 PM
CAS classification : [_separable]

\begin{align*} x^{5} y^{\prime }+y^{5}&=0 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 67

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

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

✓ Mathematica. Time used: 0.724 (sec). Leaf size: 145

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

\begin{align*} y(x)\to -\frac {x}{\sqrt [4]{-1-4 c_1 x^4}} \\ y(x)\to -\frac {i x}{\sqrt [4]{-1-4 c_1 x^4}} \\ y(x)\to \frac {i x}{\sqrt [4]{-1-4 c_1 x^4}} \\ y(x)\to \frac {x}{\sqrt [4]{-1-4 c_1 x^4}} \\ y(x)\to 0 \\ y(x)\to -\frac {(1+i) x}{\sqrt {2}} \\ y(x)\to -\frac {(1-i) x}{\sqrt {2}} \\ y(x)\to \frac {(1-i) x}{\sqrt {2}} \\ y(x)\to \frac {(1+i) x}{\sqrt {2}} \\ \end{align*}

✓ Sympy. Time used: 2.226 (sec). Leaf size: 75

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

\[ \left [ y{\left (x \right )} = - i \sqrt [4]{- \frac {x^{4}}{C_{1} x^{4} + 1}}, \ y{\left (x \right )} = i \sqrt [4]{- \frac {x^{4}}{C_{1} x^{4} + 1}}, \ y{\left (x \right )} = - \sqrt [4]{- \frac {x^{4}}{C_{1} x^{4} + 1}}, \ y{\left (x \right )} = \sqrt [4]{- \frac {x^{4}}{C_{1} x^{4} + 1}}\right ] \]