Internal problem ID [11390]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }+y+\frac {1}{y}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(y(t),t)+y(t)+1/y(t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) = \sqrt {{\mathrm e}^{-2 t} c_{1} -1} y \left (t \right ) = -\sqrt {{\mathrm e}^{-2 t} c_{1} -1} \end{align*}
✓ Solution by Mathematica
Time used: 4.571 (sec). Leaf size: 57
DSolve[y'[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*}