74.4.4 problem 4

Internal problem ID [15897]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 08:17:51 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1+y^{2}}{y} \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 29

dsolve(diff(y(t),t)=(1+y(t)^2)/y(t),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: 2.362 (sec). Leaf size: 53

DSolve[D[y[t],t]==(1+y[t]^2)/y[t],y[t],t,IncludeSingularSolutions -> True]
 

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