56.1.10 problem 10

Internal problem ID [8722]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 10
Date solved : Monday, January 27, 2025 at 04:20:31 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \int \frac {\sec \left (x \right )}{x}d x +x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.733 (sec). Leaf size: 25

DSolve[D[y[x],x] == 1+Sec[x]/x,y[x],x,IncludeSingularSolutions -> True]
 

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