What is the solution for x(dy)/(dx)+cot(y)=0 ?

The solution for x(dy)/(dx)+cot(y)=0 is y=arccos(c_{1}x)+2pin,y=-arccos(c_{1}x)+2pin

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x(dy)/(dx)+cot(y)=0

x \frac{d y}{d x} + cot (y) = 0

y = arccos (c_{1} x) + 2 πn, y = - arccos (c_{1} x) + 2 πn

Solution steps

x \frac{d y}{d x} + cot (y) = 0

Solve separable ODE:

y = arccos (c_{1} x) + 2 πn, y = - arccos (c_{1} x) + 2 πn

y = arccos (c_{1} x) + 2 πn, y = - arccos (c_{1} x) + 2 πn

N^{^{'}} = r - a (N - b)^{2}

y^{^{'}} = \frac{1}{2} y cos^{2} (y)

y^{^{'}} + 2 x y = 0, y (0) = 1

\frac{d h}{d t} = - \frac{3}{100} h - 19

\frac{d x}{d t} = 50 - \frac{x}{100}, x = 3000, t = 0

What is the solution for x(dy)/(dx)+cot(y)=0 ?
The solution for x(dy)/(dx)+cot(y)=0 is y=arccos(c_{1}x)+2pin,y=-arccos(c_{1}x)+2pin