Internal problem ID [2874]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 125.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\left (1+\cos \relax (x ) \sin \relax (y)\right ) \tan \relax (y)=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x) = (1+cos(x)*sin(y(x)))*tan(y(x)),y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 1.893 (sec). Leaf size: 56
DSolve[y'[x]==(1+Cos[x] Sin[y[x]])Tan[y[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\csc ^{-1}\left (\frac {1}{2} \left (\sin (x)+\cos (x)+2 c_1 e^{-x}\right )\right ) \\ y(x)\to -\csc ^{-1}\left (\frac {1}{2} \left (\sin (x)+\cos (x)+2 c_1 e^{-x}\right )\right ) \\ y(x)\to 0 \\ \end{align*}