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

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

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(dy)/(dx)=sec(y)

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = 3 x^{2} y^{2}, y (- 1) = a, y (0) = 1

3 d x + y d y = 0

\frac{d y}{d x} = \frac{x y - 4 x + y - 4}{x y - 6 x - 3 y + 18}

\frac{d y}{d x} = x^{2} (y - 2), y (0) = 4

y^{^{'}} = e^{- y}, y (0) = 0

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