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

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

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cos(2y)dy=dx

cos (2 y) d y = d x

y = \frac{arcsin ( 2 x + c _{1} )}{2} + πn, y = \frac{π}{2} + \frac{arcsin ( - 2 x - c _{1} )}{2} + πn

Solution steps

cos (2 y) d y = d x

Solve separable ODE:

y = \frac{arcsin ( 2 x + c _{1} )}{2} + πn, y = \frac{π}{2} + \frac{arcsin ( - 2 x - c _{1} )}{2} + πn

y = \frac{arcsin ( 2 x + c _{1} )}{2} + πn, y = \frac{π}{2} + \frac{arcsin ( - 2 x - c _{1} )}{2} + πn

y d x + (x - 1) d y = 0, y (2) = 25

2 y y^{^{'}} = 18 t^{2}, y (0) = 7

\frac{d y}{d t} + 2 y = 5, y (0) = 1

\frac{d y}{d x} = \frac{3 x + x y ^{2}}{2 y + x ^{2} y}, y (2) = 1

\frac{d y}{d x} = 800 y

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