1. pmms12585

    Request for help with tricky Riccati DE with exponential terms.

    Hi all, I am developing a model that requires me to derive the solution of a rather tricky Riccati DE, and I am having a devil of a time with it and am beginning to wonder if there is even a closed-form solution. Anyhow, the equation is \frac{dE}{dt} = cB_{t} + bE_{t} + aE_{t}^{2}...
  2. M

    riccati equation

    show that any function y of the type (Cf1+f2)/(Cf3+f4) where f1, f2, f3, f4 are functions of x and C is an arbitrary constant, satisfies a Riccati equation
  3. M

    Riccati equation

    find the general solution to the differential equation (y+1)/x - (y^2/x^3) sorry about the aesthetically unappealing format by which i have shown this :p thanks in advance!
  4. A

    Riccati Equation to Bernoulli to Linear

    I was working the attached problem which asked that one demonstrate that a Riccati equation was reducible to a Bernoulli with the given substitution and then to bring that down to a linear equation. Can someone please explain why the signs change from the 2nd to last to the last step? Thank you...
  5. T

    differential Equations system Riccati

    I need your help. I don't want to compute this in matlab. I want an analytical solution, like old times when you were students. \begin{equation} \psi^\chi(u,x,t,T) = e^{\alpha(t) + \beta(t)\cdot x} , \end{equation} where $\beta(t)$ et $\alpha(t)$ solve \begin{equation} \begin{cases}...
  6. C

    Bernoulli / Riccati Equation

    Hello, I have an equation of the following form: y'(t) + Ay(t) + By(t)^m + c = 0 1/ With c=0, the equation is of the Bernoulli form, and might be integrated. 2/ With m = 2, it is a Riccati equation, which might be turn back to a Bernoulli one and then integrated 3/ My question is about the...
  7. B

    Riccati Equation - URGENT

    Please, can anybody help me to solve these two equations? Is this Riccati Equation? I think it is but I can’t find particular solution… y’=y^2 + yx^3 – xy – x^4. My main task is to find initial x0 and y0 so that the equation can have vertical asymptote. How to solve (x^2y^2 +...