How to Integrate an ODE

Hi Everyone,

I have a problem I was hoping to get help with. I have an ODE (shown below) and I need to find theta (Represented with O) for 3 beta (B) cases. All information is shown below.

Where: B = 0,0.3, and 0.9

v = 1*10^-4

l = 1

u = 1

Boundary condition is O = 0 at x = 0

I was trying to use ODE45 but I couldn't figure out how to manipulate the function to deal with both U and O. Essentially I have to make a macro that can find O when given the appropriate B value. Any guidance into how I would go about working with this ode would be much appreciated! Thank you!

Answer 1

[Torsten]

U^6(x)*O^2(x) - U^6(0)*O^2(0) = 0.45*nu*integral_{x=0}^{x=x} U^5(x) dx

Solve for O(x).