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:

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!