Internal problem ID [11380]
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: 1(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{2}=1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 8
dsolve(diff(y(t),t)=1+y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = \tan \left (t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.216 (sec). Leaf size: 24
DSolve[y'[t]==1+y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \tan (t+c_1) y(t)\to -i y(t)\to i \end{align*}