What is the solution for (dy)/(dx)=(x-6)e^{-2y},y(6)=ln(6) ?

The solution for (dy)/(dx)=(x-6)e^{-2y},y(6)=ln(6) is y=(ln(x^2-12x+72))/2

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(dy)/(dx)=(x-6)e^{-2y},y(6)=ln(6)

\frac{d y}{d x} = (x - 6) e^{- 2 y}, y (6) = ln (6)

y = \frac{ln ( x ^{2} - 12 x + 72 )}{2}

Solution steps

\frac{d y}{d x} = (x - 6) e^{- 2 y}

Solve separable ODE:

y = \frac{ln ( x ^{2} - 12 x + 72 )}{2}

y = \frac{ln ( x ^{2} - 12 x + 72 )}{2}

0 = \frac{1}{10} y + (100 \cdot 1 0^{- 3}) y^{^{'}}

\frac{d Q}{d t} + \frac{2}{300} Q = 0.8

y^{^{'}} - (1 + tan^{2} (x)) y = 0

2 \frac{d y}{d x} - \frac{1}{y} = \frac{2 x}{y}

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

What is the solution for (dy)/(dx)=(x-6)e^{-2y},y(6)=ln(6) ?
The solution for (dy)/(dx)=(x-6)e^{-2y},y(6)=ln(6) is y=(ln(x^2-12x+72))/2