73.1.39 problem 2.7 c

Internal problem ID [14946]
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 : Monday, March 31, 2025 at 01:04:42 PM
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*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 10

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

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

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

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

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

✓ Sympy. Time used: 0.163 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1/(x**2 + 1),0) 
ics = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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