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

The solution for (xtan(y/x)+y)*dx-x*dy=0 is y=arcsin(c_{1}x)x+2pinx,y=pix+arcsin(-c_{1}x)x+2pinx

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

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

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

Solution steps

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

Solve using substitution:

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

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

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What is the solution for (xtan(y/x)+y)*dx-x*dy=0 ?
The solution for (xtan(y/x)+y)*dx-x*dy=0 is y=arcsin(c_{1}x)x+2pinx,y=pix+arcsin(-c_{1}x)x+2pinx