What is the solution for y^'=(sin(x))/(sin(y)) ?

The solution for y^'=(sin(x))/(sin(y)) is y=arccos(cos(x)-c_{1})+2pin,y=-arccos(cos(x)-c_{1})+2pin

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y^'=(sin(x))/(sin(y))

y^{^{'}} = \frac{sin ( x )}{sin ( y )}

y = arccos (cos (x) - c_{1}) + 2 πn, y = - arccos (cos (x) - c_{1}) + 2 πn

Solution steps

y^{'} (x) = \frac{sin ( x )}{sin ( y )}

Solve separable ODE:

y = arccos (cos (x) - c_{1}) + 2 πn, y = - arccos (cos (x) - c_{1}) + 2 πn

y = arccos (cos (x) - c_{1}) + 2 πn, y = - arccos (cos (x) - c_{1}) + 2 πn

\frac{d y}{d x} = \frac{x}{y ^{2}} + x y, y (1) = 1

y^{^{'}} - e^{- y} sec^{2} (x) = 0

\frac{d y}{d x} = (1 + 2 y - 1)^{2}

\frac{d}{d t} ((x) (t)) = 2 x

(1 + cos^{2} (x)) y^{^{'}} + 2 y cos (x) sin (x) = 0

What is the solution for y^'=(sin(x))/(sin(y)) ?
The solution for y^'=(sin(x))/(sin(y)) is y=arccos(cos(x)-c_{1})+2pin,y=-arccos(cos(x)-c_{1})+2pin