What is the solution for derivative of xcos(y)=5 ?

The solution for derivative of xcos(y)=5 is y=arccos((5x+c_{1})/x)+2pin,y=-arccos((5x+c_{1})/x)+2pin

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derivative of xcos(y)=5

\frac{d}{d x} (x cos (y)) = 5

y = arccos (\frac{5 x + c _{1}}{x}) + 2 πn, y = - arccos (\frac{5 x + c _{1}}{x}) + 2 πn

Solution steps

\frac{d}{d x} (x cos (y)) = 5

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

then

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

x cos (y) = \int 5 d x

\int 5 d x = 5 x + c_{1}

x cos (y) = 5 x + c_{1}

Isolate

y : y = arccos (\frac{5 x + c _{1}}{x}) + 2 πn, y = - arccos (\frac{5 x + c _{1}}{x}) + 2 πn

y = arccos (\frac{5 x + c _{1}}{x}) + 2 πn, y = - arccos (\frac{5 x + c _{1}}{x}) + 2 πn

\frac{d y}{d x} = (x e^{y}), y (0) = 1

y^{^{'}} = 4 x^{2} + x^{2} y^{2}

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

y^{^{'}} - 4 y^{^{'}} + 3 y = 0

\frac{d y}{d t} + 12 y = - 15

What is the solution for derivative of xcos(y)=5 ?
The solution for derivative of xcos(y)=5 is y=arccos((5x+c_{1})/x)+2pin,y=-arccos((5x+c_{1})/x)+2pin