50.1.10 problem 10

Internal problem ID [10008]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 06:46:18 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x) = 1+sec(x)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \int \frac {\sec \left (x \right )}{x}d x +x +c_1 \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 25

ode=D[y[x],x] == 1+Sec[x]/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x\left (\frac {\sec (K[1])}{K[1]}+1\right )dK[1]+c_1 \end{align*}

✓ Sympy. Time used: 0.952 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} + \int \frac {x \cos {\left (x \right )} + 1}{x \cos {\left (x \right )}}\, dx \]