What is the solution for (dy)/(dx)=(x-4)e^{-2y} ?

The solution for (dy)/(dx)=(x-4)e^{-2y} is y=(ln(x^2-8x+c_{1}))/2

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(dy)/(dx)=(x-4)e^{-2y}

\frac{d y}{d x} = (x - 4) e^{- 2 y}

y = \frac{ln ( x ^{2} - 8 x + c _{1} )}{2}

Solution steps

\frac{d y}{d x} = (x - 4) e^{- 2 y}

Solve separable ODE:

y = \frac{ln ( x ^{2} - 8 x + c _{1} )}{2}

y = \frac{ln ( x ^{2} - 8 x + c _{1} )}{2}

y^{^{'}} = 6 x^{2} \cdot y

\int 4 e^{- 7 x} d x

f (x) = \frac{x ^{3} + 5}{x}

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\int_{\frac{1}{2}}^{1} (x^{- 3} - 21) d x

What is the solution for (dy)/(dx)=(x-4)e^{-2y} ?
The solution for (dy)/(dx)=(x-4)e^{-2y} is y=(ln(x^2-8x+c_{1}))/2