What is the solution for x(dy)/(dx)=tan(y) ?

The solution for x(dy)/(dx)=tan(y) is y=arcsin(c_{1}x)+2pin,y=pi+arcsin(-c_{1}x)+2pin

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x(dy)/(dx)=tan(y)

x \frac{d y}{d x} = tan (y)

y = arcsin (c_{1} x) + 2 πn, y = π + arcsin (- c_{1} x) + 2 πn

Solution steps

x \frac{d y}{d x} = tan (y)

Solve separable ODE:

y = arcsin (c_{1} x) + 2 πn, y = π + arcsin (- c_{1} x) + 2 πn

y = arcsin (c_{1} x) + 2 πn, y = π + arcsin (- c_{1} x) + 2 πn

y^{^{'}} = \frac{x x ^{2} - 1}{y}

y^{^{'}} = 3 x y

\frac{d y}{d x} + 3 x^{2} y = 5 x^{2}

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

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

What is the solution for x(dy)/(dx)=tan(y) ?
The solution for x(dy)/(dx)=tan(y) is y=arcsin(c_{1}x)+2pin,y=pi+arcsin(-c_{1}x)+2pin