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

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

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

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

y = \frac{arctan ( x + \frac{1}{2} sin ( 2 x ) + c _{1} )}{2} + \frac{πn}{2}

Solution steps

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

Solve separable ODE:

y = \frac{arctan ( x + \frac{1}{2} sin ( 2 x ) + c _{1} )}{2} + \frac{πn}{2}

y = \frac{arctan ( x + \frac{1}{2} sin ( 2 x ) + c _{1} )}{2} + \frac{πn}{2}

y^{^{'}} = \frac{x}{y}, y (0) = 0

y^{^{'}} = \frac{7 x ^{2} - 1}{7 + 5 y}

y^{^{'}} = \frac{x ( 1 + y ^{2} )}{4 y}

\frac{d y}{d x} y = (ln (x))^{l n (x)}

y^{^{'}} = \frac{5 x + 8}{y}

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