29.5.3 problem 118

Internal problem ID [4720]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 118
Date solved : Monday, January 27, 2025 at 09:33:59 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\tan \left (x \right ) \cot \left (y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.246 (sec). Leaf size: 9

dsolve(diff(y(x),x)+tan(x)*cot(y(x)) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \arccos \left (\sec \left (x \right ) c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 6.038 (sec). Leaf size: 47

DSolve[D[y[x],x]+Tan[x] Cot[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\arccos \left (\frac {1}{2} c_1 \sec (x)\right ) \\ y(x)\to \arccos \left (\frac {1}{2} c_1 \sec (x)\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}