29.5.1 problem 116

Internal problem ID [4718]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 116
Date solved : Monday, January 27, 2025 at 09:33:54 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.239 (sec). Leaf size: 14

dsolve(diff(y(x),x) = sin(x)*(csc(y(x))-cot(y(x))),y(x), singsol=all)
 

\[ y \left (x \right ) = \arccos \left (c_{1} {\mathrm e}^{-\cos \left (x \right )}+1\right ) \]

✓ Solution by Mathematica

Time used: 0.419 (sec). Leaf size: 70

DSolve[D[y[x],x]==Sin[x](Csc[y[x]]-Cot[y[x]]),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \cos (x) \tan \left (\frac {y(x)}{2}\right ) e^{\text {arctanh}(\cos (y(x)))}-\sqrt {\sin ^2(y(x))} \csc \left (\frac {y(x)}{2}\right ) \sec \left (\frac {y(x)}{2}\right ) \left (\log \left (\sec ^2\left (\frac {y(x)}{2}\right )\right )-2 \log \left (\tan \left (\frac {y(x)}{2}\right )\right )\right )=c_1,y(x)\right ] \]