Internal problem ID [13816]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number: 12.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=\frac {1}{t^{2}+1}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 6
dsolve([diff(y(t),t)=1/(1+t^2),y(0) = 0],y(t), singsol=all)
\[ y = \arctan \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 7
DSolve[{y'[t]==1/(1+t^2),{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \arctan (t) \]