What is the solution for (dy)/(dx)=(e^x)/(cos(y)) ?

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

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(dy)/(dx)=(e^x)/(cos(y))

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

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

Solution steps

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

Solve separable ODE:

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

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

7 x y (\frac{d y}{d x}) = 3

y^{^{'}} = e^{y} 5^{x}, y (0) = ln (ln (5))

y^{^{'}} = - 10 x^{2} y

x^{3} y^{^{'}} + (5 x^{2} - 8) y = 0

3 y^{^{'}} - y = 0

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