Internal problem ID [6139]
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]
\[ \boxed {y^{\prime } x^{5}+y^{5}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 67
dsolve(x^5*diff(y(x),x)+y(x)^5=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x}{\left (c_{1} x^{4}-1\right )^{\frac {1}{4}}} \\ y \left (x \right ) &= -\frac {x}{\left (c_{1} x^{4}-1\right )^{\frac {1}{4}}} \\ y \left (x \right ) &= \frac {x}{\sqrt {-\sqrt {c_{1} x^{4}-1}}} \\ y \left (x \right ) &= -\frac {x}{\sqrt {-\sqrt {c_{1} x^{4}-1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.489 (sec). Leaf size: 145
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 -\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*}