10.1.14 problem 3(h)

Internal problem ID [3416]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 3(h)
Date solved : Tuesday, September 30, 2025 at 06:37:54 AM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 8

ode:=(x^2+1)*diff(y(x),x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arctan \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 10

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

\begin{align*} y(x)&\to \arctan (x)+c_1 \end{align*}

✓ Sympy. Time used: 0.095 (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 = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \operatorname {atan}{\left (x \right )} \]