63.4.13 problem 4(e)

Internal problem ID [13056]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page 26
Problem number : 4(e)
Date solved : Tuesday, January 28, 2025 at 04:50:25 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y+\frac {1}{y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 29

dsolve(diff(y(t),t)+y(t)+1/y(t)=0,y(t), singsol=all)
 

\begin{align*} y &= \sqrt {c_{1} {\mathrm e}^{-2 t}-1} \\ y &= -\sqrt {c_{1} {\mathrm e}^{-2 t}-1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 2.440 (sec). Leaf size: 57

DSolve[D[y[t],t]+y[t]+1/y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to -\sqrt {-1+e^{-2 t+2 c_1}} \\ y(t)\to \sqrt {-1+e^{-2 t+2 c_1}} \\ y(t)\to -i \\ y(t)\to i \\ \end{align*}