74.4.51 problem 51

Internal problem ID [15944]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 51
Date solved : Tuesday, January 28, 2025 at 08:24:07 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 8

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

\[ y = \arctan \left (x \right )+1 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 22

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

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