Internal problem ID [4410]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x -\frac {1}{y^{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 53
dsolve(x*diff(y(x),x)=1/y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \left (4 \ln \relax (x )+c_{1}\right )^{\frac {1}{4}} \\ y \relax (x ) = -\left (4 \ln \relax (x )+c_{1}\right )^{\frac {1}{4}} \\ y \relax (x ) = -i \left (4 \ln \relax (x )+c_{1}\right )^{\frac {1}{4}} \\ y \relax (x ) = i \left (4 \ln \relax (x )+c_{1}\right )^{\frac {1}{4}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.227 (sec). Leaf size: 84
DSolve[x*y'[x]==1/y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} \sqrt [4]{\log (x)+c_1} \\ y(x)\to -i \sqrt {2} \sqrt [4]{\log (x)+c_1} \\ y(x)\to i \sqrt {2} \sqrt [4]{\log (x)+c_1} \\ y(x)\to \sqrt {2} \sqrt [4]{\log (x)+c_1} \\ \end{align*}