What is the solution for (dy)/(dx)=(x-8)e^{-2y},y(8)=ln(8) ?

The solution for (dy)/(dx)=(x-8)e^{-2y},y(8)=ln(8) is y=(ln(x^2-16x+128))/2

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(dy)/(dx)=(x-8)e^{-2y},y(8)=ln(8)

\frac{d y}{d x} = (x - 8) e^{- 2 y}, y (8) = ln (8)

y = \frac{ln ( x ^{2} - 16 x + 128 )}{2}

Solution steps

\frac{d y}{d x} = (x - 8) e^{- 2 y}

Solve separable ODE:

y = \frac{ln ( x ^{2} - 16 x + 128 )}{2}

y = \frac{ln ( x ^{2} - 16 x + 128 )}{2}

\frac{d}{d x} (tan^{4} (x))

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

\int 3 tan^{3} (θ) d θ

y^{^{'}} = x y^{2} (1 + x^{2})^{- \frac{1}{2}}, y (0) = 2

(4, 1), (6, 7)

What is the solution for (dy)/(dx)=(x-8)e^{-2y},y(8)=ln(8) ?
The solution for (dy)/(dx)=(x-8)e^{-2y},y(8)=ln(8) is y=(ln(x^2-16x+128))/2