Internal problem ID [14162]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\frac {1+y^{2}}{y}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 29
dsolve(diff(y(t),t)=(1+y(t)^2)/y(t),y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \sqrt {c_{1} {\mathrm e}^{2 t}-1} \\ y \left (t \right ) &= -\sqrt {c_{1} {\mathrm e}^{2 t}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.441 (sec). Leaf size: 53
DSolve[y'[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*}