36.1.7 problem 7

Internal problem ID [6262]
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
Date solved : Monday, January 27, 2025 at 01:50:25 PM
CAS classification : [_separable]

\begin{align*} x y^{\prime }&=\frac {1}{y^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 51

dsolve(x*diff(y(x),x)=1/y(x)^3,y(x), singsol=all)
 

\begin{align*} y &= \left (4 \ln \left (x \right )+c_{1} \right )^{{1}/{4}} \\ y &= -\left (4 \ln \left (x \right )+c_{1} \right )^{{1}/{4}} \\ y &= -i \left (4 \ln \left (x \right )+c_{1} \right )^{{1}/{4}} \\ y &= i \left (4 \ln \left (x \right )+c_{1} \right )^{{1}/{4}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 84

DSolve[x*D[y[x],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*}