What is the solution for derivative of x*cos(y)=1 ?

The solution for derivative of x*cos(y)=1 is y=arccos((x+c_{1})/x)+2pin,y=-arccos((x+c_{1})/x)+2pin

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derivative of x*cos(y)=1

\frac{d}{d x} (x \cdot cos (y)) = 1

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

Solution steps

\frac{d}{d x} (x \cdot cos (y)) = 1

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

x cos (y) = \int 1 d x

\int 1 d x = x + c_{1}

x cos (y) = x + c_{1}

Isolate

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

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

y^{^{'}} = \frac{x y}{y + 1}

y^{^{'}} = u - y

y^{^{'}} = y^{2} + 2 y + 1

\frac{y ^{^{'}}}{x} = 4 y

y^{3} \frac{d y}{d x} = - x^{4}

What is the solution for derivative of x*cos(y)=1 ?
The solution for derivative of x*cos(y)=1 is y=arccos((x+c_{1})/x)+2pin,y=-arccos((x+c_{1})/x)+2pin