What is the solution for 2xdx+x^2cot(y)dy=0 ?

The solution for 2xdx+x^2cot(y)dy=0 is y=arcsin((c_{1})/(x^2))+2pin,y=pi+arcsin(-(c_{1})/(x^2))+2pin

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2xdx+x^2cot(y)dy=0

2 x d x + x^{2} cot (y) d y = 0

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

Solution steps

2 x d x + x^{2} cot (y) d y = 0

Solve separable ODE:

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

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

y^{^{'}} - \frac{2 y}{x} = \frac{y ^{^{'}}}{x}

\frac{d x}{d t} = 100 - \frac{x}{100}

(1 + x) y d x + (1 - y) x d y = 0

\frac{d y}{d x} = y x^{2}

\frac{d r}{d s} = e^{r - 2 s}, r (0) = 0

What is the solution for 2xdx+x^2cot(y)dy=0 ?
The solution for 2xdx+x^2cot(y)dy=0 is y=arcsin((c_{1})/(x^2))+2pin,y=pi+arcsin(-(c_{1})/(x^2))+2pin