50.2.1 problem 1(a)

Internal problem ID [7807]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 1(a)
Date solved : Monday, January 27, 2025 at 03:23:34 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 67

dsolve(x^5*diff(y(x),x)+y(x)^5=0,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*}

✓ Solution by Mathematica

Time used: 0.746 (sec). Leaf size: 145

DSolve[x^5*D[y[x],x]+y[x]^5==0,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*}