56.1.1 problem 1

Internal problem ID [8713]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 1
Date solved : Monday, January 27, 2025 at 04:20:04 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.096 (sec). Leaf size: 73

dsolve(diff(y(x),x) = cos(y(x))*sec(x)/x,y(x), singsol=all)
 

\[ y = \arctan \left (\frac {{\mathrm e}^{2 \left (\int \frac {\sec \left (x \right )}{x}d x \right )} c_{1}^{2}-1}{{\mathrm e}^{2 \left (\int \frac {\sec \left (x \right )}{x}d x \right )} c_{1}^{2}+1}, \frac {2 \,{\mathrm e}^{\int \frac {\sec \left (x \right )}{x}d x} c_{1}}{{\mathrm e}^{2 \left (\int \frac {\sec \left (x \right )}{x}d x \right )} c_{1}^{2}+1}\right ) \]

✓ Solution by Mathematica

Time used: 2.190 (sec). Leaf size: 49

DSolve[D[y[x],x]== Cos[y[x]]*Sec[x]/x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2 \arctan \left (\tanh \left (\frac {1}{2} \left (\int _1^x\frac {\sec (K[1])}{K[1]}dK[1]+c_1\right )\right )\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}