What is the solution for e^{-y}cos(x)-(dy)/(dx)=0 ?

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

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e^{-y}cos(x)-(dy)/(dx)=0

e^{- y} cos (x) - \frac{d y}{d x} = 0

y = ln (sin (x) + c_{1})

Solution steps

e^{- y} cos (x) - \frac{d y}{d x} = 0

Solve separable ODE:

y = ln (sin (x) + c_{1})

y = ln (sin (x) + c_{1})

y y^{^{'}} = 3 x^{2} 16 + y^{2}

y + y^{^{'}} arcsin (x) = 0

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

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

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

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