13.3.1 problem 1

Internal problem ID [2318]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.4. Page 24
Problem number : 1
Date solved : Monday, January 27, 2025 at 05:45:29 AM
CAS classification : [_separable]

\begin{align*} \left (t^{2}+1\right ) y^{\prime }&=1+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 9

dsolve((t^2+1)*diff(y(t),t) = 1+y(t)^2,y(t), singsol=all)
 

\[ y = \tan \left (\arctan \left (t \right )+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.261 (sec). Leaf size: 25

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

\begin{align*} y(t)\to \tan (\arctan (t)+c_1) \\ y(t)\to -i \\ y(t)\to i \\ \end{align*}