Internal problem ID [6292]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\cos \relax (y) \sec \relax (x )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.167 (sec). Leaf size: 81
dsolve(diff(y(x),x) = cos(y(x))*sec(x)/x,y(x), singsol=all)
\[ y \relax (x ) = \arctan \left (\frac {{\mathrm e}^{2 \left (\int \frac {1}{\cos \relax (x ) x}d x \right )} c_{1}^{2}-1}{{\mathrm e}^{2 \left (\int \frac {1}{\cos \relax (x ) x}d x \right )} c_{1}^{2}+1}, \frac {2 \,{\mathrm e}^{\int \frac {1}{\cos \relax (x ) x}d x} c_{1}}{{\mathrm e}^{2 \left (\int \frac {1}{\cos \relax (x ) x}d x \right )} c_{1}^{2}+1}\right ) \]
✓ Solution by Mathematica
Time used: 4.219 (sec). Leaf size: 49
DSolve[y'[x]== Cos[y[x]]*Sec[x]/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \text {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*}