What is the solution for (dy)/(dx)=cos^2(y), pi/2 <y ?

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

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(dy)/(dx)=cos^2(y), pi/2 <y

\frac{d y}{d x} = cos^{2} (y), \frac{π}{2} < y

y = arctan (x + c_{1}) + πn

Solution steps

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

Solve separable ODE:

y = arctan (x + c_{1}) + πn

y = arctan (x + c_{1}) + πn

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

y^{^{'}} + 2 x \cdot y = 0

2 y (y^{^{'}}) = 6 t^{2}, y (0) = 5

P^{^{'}} = 0.05 P (1 - \frac{P}{400})

y = 5 (sin^{2} (x)) y^{^{'}}

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