Recent content by Rruffpaw

  1. R

    Graduate Extension of Variation of Parameters to First Order Non-Linear ODE?

    Thanks again! You are right in that I too missed the k^2 in the denominator (amongst other typos) I will recheck everything and formally derive the solution which I will post. Cheers, -Sharat
  2. R

    Graduate Extension of Variation of Parameters to First Order Non-Linear ODE?

    JJacquelin, Many thanks again for your help. Could you kindly review the attached where I've re-derived the last step (I think you had a k in the coefficient of df/dT in your last equation that should not be there) and compared it to a transformed version of Bessel's Differential Equation from...
  3. R

    Graduate Extension of Variation of Parameters to First Order Non-Linear ODE?

    Thanks! This looks neat. But what about the initial conditions for f and f'? I could of course solve the 2nd order linear ODE and substitute f and f' back into the expression for V, but I'll have two constants and only one initial condition. Or do I apply the condition (f'=0 at T=0 which...
  4. R

    Graduate Extension of Variation of Parameters to First Order Non-Linear ODE?

    The equation of motion of a rocket with mass depletion during ascent and subject to drag forces can be written as M(t) dV/dt = A - M(t)g - BV^2 (Eq. 1) with initial condition V(t=0) = 0 (V is velocity and t is time) Let us assume a linear mass depletion according to...
    • Rruffpaw
    • Thread
    • Extension First order Non-linear Ode Parameters Variation Variation of parameters
    • Replies: 7
    • Forum: Differential Equations