Internal problem ID [4918]
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]
\[ \boxed {x y^{\prime }-\frac {1}{y^{3}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
dsolve(x*diff(y(x),x)=1/y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (4 \ln \left (x \right )+c_{1} \right )^{\frac {1}{4}} \\ y \left (x \right ) &= -\left (4 \ln \left (x \right )+c_{1} \right )^{\frac {1}{4}} \\ y \left (x \right ) &= -i \left (4 \ln \left (x \right )+c_{1} \right )^{\frac {1}{4}} \\ y \left (x \right ) &= i \left (4 \ln \left (x \right )+c_{1} \right )^{\frac {1}{4}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.15 (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*}