1. ## Integration help

Hi everyone

I have some homework due in a day and i can't understand this question...

consider the differential equation: 2xy(dy/dx)=y^2-9, x≠0

1a) find the steady state solutions(if any)

b) find the general solution

c) Find the particular solution satisfying y=5 when x=4

Any help would be appreciated thanks already!

2. Part a can be solved fairly easily by understanding that a "steady state solution" means that dy/dx=0. So substitute dy/dx=0 into the equation and solve it for y.

For the rest of the question, first check that you have copied it down correctly. A well placed minus sign would make the problem very much easier!

3. $\displaystyle 2xy\dfrac{dy}{dx} = y^2 - 9$
$\displaystyle \Rightarrow \dfrac{2ydy}{y^2 - 9} = \dfrac{dx}{x}$
$\displaystyle \\\Rightarrow \ln(y^2 - 9) = \ln x + C$
$\displaystyle \\y^2 - 9 = xe^C$
$\displaystyle \\y^2 = 9 + xe^C$
$\displaystyle \\y = \pm \sqrt{9 + xe^C}$
sub in the numbers and you get
$\displaystyle \\y = \sqrt{9 + 4x}$