Internal problem ID [5386]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x^{5}+y^{5}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.033 (sec). Leaf size: 67
dsolve(x^5*diff(y(x),x)+y(x)^5=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {x}{\left (c_{1} x^{4}-1\right )^{\frac {1}{4}}} \\ y \relax (x ) = -\frac {x}{\left (c_{1} x^{4}-1\right )^{\frac {1}{4}}} \\ y \relax (x ) = \frac {x}{\sqrt {-\sqrt {c_{1} x^{4}-1}}} \\ y \relax (x ) = -\frac {x}{\sqrt {-\sqrt {c_{1} x^{4}-1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.355 (sec). Leaf size: 135
DSolve[x^5*y'[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 -\sqrt [4]{-1} x \\ y(x)\to (-1)^{3/4} x \\ y(x)\to -(-1)^{3/4} x \\ y(x)\to \sqrt [4]{-1} x \\ \end{align*}