What is the solution for (dy)/(dx)=(x-3)e^{-2y},y(3)=ln(3) ?

The solution for (dy)/(dx)=(x-3)e^{-2y},y(3)=ln(3) is y=(ln(x^2-6x+18))/2

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(dy)/(dx)=(x-3)e^{-2y},y(3)=ln(3)

\frac{d y}{d x} = (x - 3) e^{- 2 y}, y (3) = ln (3)

y = \frac{ln ( x ^{2} - 6 x + 18 )}{2}

Solution steps

\frac{d y}{d x} = (x - 3) e^{- 2 y}

Solve separable ODE:

y = \frac{ln ( x ^{2} - 6 x + 18 )}{2}

y = \frac{ln ( x ^{2} - 6 x + 18 )}{2}

What is the solution for (dy)/(dx)=(x-3)e^{-2y},y(3)=ln(3) ?
The solution for (dy)/(dx)=(x-3)e^{-2y},y(3)=ln(3) is y=(ln(x^2-6x+18))/2