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

The solution for (dx)/(dy)=sin(x)(cos(2y)-cos^2(y)) is x=2arctan(e^{-1/2 y+1/4 sin(2y)+c_{1}})+2pin

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(dx)/(dy)=sin(x)(cos(2y)-cos^2(y))

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

x = 2 arctan (e^{- \frac{1}{2} y + \frac{1}{4} s i n (2 y) + c_{1}}) + 2 πn

Solution steps

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

Solve separable ODE:

x = 2 arctan (e^{- \frac{1}{2} y + \frac{1}{4} s i n (2 y) + c_{1}}) + 2 πn

x = 2 arctan (e^{- \frac{1}{2} y + \frac{1}{4} s i n (2 y) + c_{1}}) + 2 πn

\frac{d}{d θ} (f (θ)) f (θ) = sin (θ) + csc (θ)

4 ln (x) d x - x sec^{2} (y) d y = 0

6 x^{2} d x - 2 y d y = 0

\frac{d y}{d x} 2 x y = 1

\frac{d Q}{d x} = 15 - 3 \frac{Q}{400}

What is the solution for (dx)/(dy)=sin(x)(cos(2y)-cos^2(y)) ?
The solution for (dx)/(dy)=sin(x)(cos(2y)-cos^2(y)) is x=2arctan(e^{-1/2 y+1/4 sin(2y)+c_{1}})+2pin