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

(1 + x^{2}) y^{^{'}} - 2 x (y + 3) = 0

\frac{d y}{d x} = y + 7

\frac{d x}{d t} = 14 - 0.28 \cdot x

\frac{d x}{d t} = \frac{8 \cdot 1 0 ^{- 3}}{100} - 8 \frac{x}{9500}

\frac{d y}{d t} = \frac{3 t ^{2}}{8 y}

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