What is the solution for csc^3(x)(dy)/(dx)=cos^2(y) ?

The solution for csc^3(x)(dy)/(dx)=cos^2(y) is y=arctan(-cos(x)+(cos^3(x))/3+c_{1})+pin

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csc^3(x)(dy)/(dx)=cos^2(y)

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

y = arctan (- cos (x) + \frac{cos ^{3} ( x )}{3} + c_{1}) + πn

Solution steps

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

Solve separable ODE:

y = arctan (- cos (x) + \frac{cos ^{3} ( x )}{3} + c_{1}) + πn

y = arctan (- cos (x) + \frac{cos ^{3} ( x )}{3} + c_{1}) + πn

y^{^{'}} = - e^{- x} y

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

3 y^{^{'}} + 2 y = 7, y (0) = 2

2 cos (y^{2}) d x - x y sin (y^{2}) d y = 0

\frac{d y}{d x} - e^{x - y} = 0

What is the solution for csc^3(x)(dy)/(dx)=cos^2(y) ?
The solution for csc^3(x)(dy)/(dx)=cos^2(y) is y=arctan(-cos(x)+(cos^3(x))/3+c_{1})+pin