What is the solution for y^'=xsin(y) ?

The solution for y^'=xsin(y) is y=2arctan(e^{(x^2)/2+c_{1}})+2pin

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y^'=xsin(y)

y^{^{'}} = x sin (y)

y = 2 arctan (e^{\frac{x ^{2}}{2} + c_{1}}) + 2 πn

Solution steps

y^{'} (x) = x sin (y)

Solve separable ODE:

y = 2 arctan (e^{\frac{x ^{2}}{2} + c_{1}}) + 2 πn

y = 2 arctan (e^{\frac{x ^{2}}{2} + c_{1}}) + 2 πn

\frac{d x}{d t} = 30 - \frac{x}{100}, x = 2000, t = 0

(x - 2) y^{^{'}} = y

\frac{d y}{d t} = 4 y - 8, y (0) = y^{0}

\frac{d S}{d t} = 0.04 - \frac{1}{600} S

\frac{d y}{d t} + \frac{t}{y ( t ^{2} - 1 )} = 0

What is the solution for y^'=xsin(y) ?
The solution for y^'=xsin(y) is y=2arctan(e^{(x^2)/2+c_{1}})+2pin