74.3.11 problem 12

Internal problem ID [15871]
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
Date solved : Tuesday, January 28, 2025 at 08:10:53 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{t^{2}+1} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (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: 20

DSolve[{D[y[t],t]==1/(1+t^2),{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _0^t\frac {1}{K[1]^2+1}dK[1] \]