73.1.39 problem 2.7 c

Internal problem ID [15017]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.7 c
Date solved : Tuesday, January 28, 2025 at 07:27:37 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 20

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

\[ y(x)\to \int _1^x\frac {1}{K[1]^2+1}dK[1] \]