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