What is the solution for (e^y+1)cos(x)dx+e^ysin(x)dy=0 ?

The solution for (e^y+1)cos(x)dx+e^ysin(x)dy=0 is y=ln((c_{1})/(sin(x))-1)

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(e^y+1)cos(x)dx+e^ysin(x)dy=0

(e^{y} + 1) cos (x) d x + e^{y} sin (x) d y = 0

y = ln (\frac{c _{1}}{sin ( x )} - 1)

Solution steps

(e^{y} + 1) cos (x) d x + e^{y} sin (x) d y = 0

Solve separable ODE:

y = ln (\frac{c _{1}}{sin ( x )} - 1)

y = ln (\frac{c _{1}}{sin ( x )} - 1)

y \cdot e^{- x} d x - e^{- x} d y = 0

\frac{d y}{d x} - 2 y = 6

tan (x) sin^{3} (y) d x + sec^{3} (x) cos (y) d y = 0

y^{^{'}} csc (t) = - \frac{y ^{3}}{2}

\frac{d y}{d x} = 1 - x + y - x y, y (0) = 0

What is the solution for (e^y+1)cos(x)dx+e^ysin(x)dy=0 ?
The solution for (e^y+1)cos(x)dx+e^ysin(x)dy=0 is y=ln((c_{1})/(sin(x))-1)