29.4.19 problem 108

Internal problem ID [4710]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 108
Date solved : Monday, January 27, 2025 at 09:32:52 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\sec \left (x \right )^{2} \cot \left (y\right ) \cos \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 11

dsolve(diff(y(x),x) = sec(x)^2*cot(y(x))*cos(y(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = \arccos \left (\frac {1}{\tan \left (x \right )+c_{1}}\right ) \]

✓ Solution by Mathematica

Time used: 0.776 (sec). Leaf size: 45

DSolve[D[y[x],x]==Sec[x]^2 Cot[y[x]] Cos[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sec ^{-1}(\tan (x)+2 c_1) \\ y(x)\to \sec ^{-1}(\tan (x)+2 c_1) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}