What is the solution for (dy)/(dx)=e^{-5y}cos(4x) ?

The solution for (dy)/(dx)=e^{-5y}cos(4x) is y=(ln(5/4 sin(4x)+c_{1}))/5

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(dy)/(dx)=e^{-5y}cos(4x)

\frac{d y}{d x} = e^{- 5 y} cos (4 x)

y = \frac{ln ( \frac{5}{4} sin ( 4 x ) + c _{1} )}{5}

Solution steps

\frac{d y}{d x} = e^{- 5 y} cos (4 x)

Solve separable ODE:

y = \frac{ln ( \frac{5}{4} sin ( 4 x ) + c _{1} )}{5}

y = \frac{ln ( \frac{5}{4} sin ( 4 x ) + c _{1} )}{5}

\frac{d y}{d x} = \frac{2}{3} x 1 - 9 y^{2}

(1 + 2 y) d x + (4 - x^{2}) d y = 0

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

\frac{y ^{^{'}}}{x} + y = 1

sin (y) + \frac{1}{2} x cos (y) \frac{d y}{d x} = 3

What is the solution for (dy)/(dx)=e^{-5y}cos(4x) ?
The solution for (dy)/(dx)=e^{-5y}cos(4x) is y=(ln(5/4 sin(4x)+c_{1}))/5