Internal problem ID [1668]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (t^{2}+1\right ) y^{\prime }-1-y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 9
dsolve((t^2+1)*diff(y(t),t) = 1+y(t)^2,y(t), singsol=all)
\[ y \relax (t ) = \tan \left (\arctan \relax (t )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.252 (sec). Leaf size: 25
DSolve[(t^2+1)*y'[t] == 1+y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \tan (\text {ArcTan}(t)+c_1) \\ y(t)\to -i \\ y(t)\to i \\ \end{align*}