What is the solution for (y+xcot(y/x))dx-xdy=0 ?

The solution for (y+xcot(y/x))dx-xdy=0 is y=arccos((c_{1})/x)x+2pinx,y=-arccos((c_{1})/x)x+2pinx

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(y+xcot(y/x))dx-xdy=0

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

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

Solution steps

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

Solve using substitution:

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

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

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