What is the solution for y^'=sin(3y) ?

The solution for y^'=sin(3y) is y=(2arctan(e^{3t+c_{1}}))/3+(2pin)/3

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y^'=sin(3y)

y^{^{'}} = sin (3 y)

y = \frac{2 arctan ( e ^{3 t + c_{1}} )}{3} + \frac{2 πn}{3}

Solution steps

y^{'} (t) = sin (3 y)

Solve separable ODE:

y = \frac{2 arctan ( e ^{3 t + c_{1}} )}{3} + \frac{2 πn}{3}

y = \frac{2 arctan ( e ^{3 t + c_{1}} )}{3} + \frac{2 πn}{3}

\frac{d y}{d x} = e^{5 y} cos (\frac{x}{2})

(x^{2} - 3) \frac{d y}{d x} - x (y - 1) = 0

x + 3 y^{2} x^{2} + 1 \frac{d y}{d x} = 0

x^{2} y \frac{d y}{d x} + 2 x y^{2} = 0

\frac{d y}{d x} = \frac{x sin ( x )}{y}, y (0) = - 1

What is the solution for y^'=sin(3y) ?
The solution for y^'=sin(3y) is y=(2arctan(e^{3t+c_{1}}))/3+(2pin)/3