What is the solution for (dy)/(dx)=e^xsin(y) ?

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

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(dy)/(dx)=e^xsin(y)

\frac{d y}{d x} = e^{x} sin (y)

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

Solution steps

\frac{d y}{d x} = e^{x} sin (y)

Solve separable ODE:

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

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

\frac{d p}{d t} = t^{2} p - 3 p + t^{2} - 3

\frac{( t ^{2} - 12 t + 11 ) d y}{d t} = y

\frac{d x}{d t} = 3 x

\frac{d y}{d x} = \frac{x ^{2} + 1}{y}

\frac{d y}{d x} = - \frac{x}{y e ^{x^{2}}}, y (0) = 1

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