Internal problem ID [591]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 \cos \relax (x ) \sin \relax (x ) \sin \relax (y)+\cos \relax (y) \left (\sin ^{2}\relax (x )\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 18
dsolve(2*cos(x)*sin(x)*sin(y(x))+cos(y(x))*sin(x)^2*diff(y(x),x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\arcsin \left (\frac {2 c_{1}}{-1+\cos \left (2 x \right )}\right ) \]
✓ Solution by Mathematica
Time used: 5.167 (sec). Leaf size: 21
DSolve[2*Cos[x]*Sin[x]*Sin[y[x]]+Cos[y[x]]*Sin[x]^2*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcSin}\left (\frac {1}{2} c_1 \csc ^2(x)\right ) \\ y(x)\to 0 \\ \end{align*}