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## Homework Statement

Find the particular solution of the differential equation dy/dx = (x-4)e^(-2y)

Satisfying initial condition y(4)=ln(4)

## Homework Equations

N/A

## The Attempt at a Solution

I separated this into dy/e^(-2y) = (x-4)dx

I then integrated it to get e^(2y)/2 = x^2/2 - 4x

I then tried to isolate y and got y= 1/2ln(x^2-8x+C)

Plugging in the values, I get ln(4)=1/2ln(-16+C)

What do I do with that 1/2 out in front? If it wasn't a part of the equation, C would equal 20. That is, if I'm correct so far.

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