79.1.3 problem 1 (iii)

Internal problem ID [18490]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 1 (iii)
Date solved : Tuesday, January 28, 2025 at 11:50:49 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} x \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.031 (sec). Leaf size: 10

dsolve([diff(x(t),t)=1/(1+t^2),x(1) = 0],x(t), singsol=all)
 

\[ x = \arctan \left (t \right )-\frac {\pi }{4} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 13

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

\[ x(t)\to \arctan (t)-\frac {\pi }{4} \]