67.1.28 problem 2.4 (f)

Internal problem ID [16293]
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 : 2.4 (f)
Date solved : Thursday, October 02, 2025 at 10:45:26 AM
CAS classification : [_quadrature]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 8

ode:=(x^2+1)*diff(y(x),x) = 1; 
ic:=[y(0) = 3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \arctan \left (x \right )+3 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 22

ode=(x^2+1)*D[y[x],x]==1; 
ic={y[0]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _0^x\frac {1}{K[1]^2+1}dK[1]+3 \end{align*}

✓ Sympy. Time used: 0.091 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**2 + 1)*Derivative(y(x), x) - 1,0) 
ics = {y(0): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \operatorname {atan}{\left (x \right )} + 3 \]