What is the solution for xy^'cos(y)+sin(y)=0 ?

The solution for xy^'cos(y)+sin(y)=0 is y=arcsin((c_{1})/x)+2pin,y=pi+arcsin(-(c_{1})/x)+2pin

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xy^'cos(y)+sin(y)=0

x y^{^{'}} cos (y) + sin (y) = 0

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

Solution steps

x y^{'} (x) cos (y) + sin (y) = 0

Solve separable ODE:

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

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

What is the solution for xy^'cos(y)+sin(y)=0 ?
The solution for xy^'cos(y)+sin(y)=0 is y=arcsin((c_{1})/x)+2pin,y=pi+arcsin(-(c_{1})/x)+2pin