Differential equation help.

Before I begin, I have to admit I'm hopeless at these things. Never gotten my head around them. Differentiation I'm okay with, but not these annoying buggers!

Question:

Consider the differential equation:

$\displaystyle 2xy.dy/dx = y^2 - 9$

a. Find the steady state solutions (if any) and the general solution.

b. Find the particular solution satisfying y = 5 when x = 4.

Well, this is my attempt at answering these questions:

rearrange the formula:

dy.1/(y² – 9) = dx.1/2xy

integrate to dy and dx:

∫y/y² – 9).dy = ∫1/2x.dx

½ln(y² - 9) = ln(x)/2 + c

ln(y² - 9) = ln(x) + 2c

e(ln(y² - 9)) = e(ln(x) + 2c)

y² - 9 = *A*x where *A* = e^2c

y² = *A*x + 9

when y = 5 and x = 4:

25 = 4*A* + 9

*A* = 4

ln(*A*) = ln(4)

c = ln(2)

Is this correct? Personally I think not based on my previous attempts at doing these sort of questions!