Internal problem ID [3374]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 116.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\sin \left (x \right ) \left (\csc \left (y\right )-\cot \left (y\right )\right )=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 14
dsolve(diff(y(x),x) = sin(x)*(csc(y(x))-cot(y(x))),y(x), singsol=all)
\[ y \left (x \right ) = \arccos \left ({\mathrm e}^{-\cos \left (x \right )} c_{1} +1\right ) \]
✓ Solution by Mathematica
Time used: 0.429 (sec). Leaf size: 70
DSolve[y'[x]==Sin[x](Csc[y[x]]-Cot[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \cos (x) \tan \left (\frac {y(x)}{2}\right ) e^{\text {arctanh}(\cos (y(x)))}-\sqrt {\sin ^2(y(x))} \csc \left (\frac {y(x)}{2}\right ) \sec \left (\frac {y(x)}{2}\right ) \left (\log \left (\sec ^2\left (\frac {y(x)}{2}\right )\right )-2 \log \left (\tan \left (\frac {y(x)}{2}\right )\right )\right )=c_1,y(x)\right ] \]