Solution of differential equations with an input derivative

How can I use ode45 in order to find a solution to differential equations with an input derivative

For example I have

    [t,x] = ode45(@fcn,[0 tmax],zeros(5,1));

    function dx = fcn(t, x)
        e = -x(1) + 1;
        dx = [(x(2)-x(1))/T2; (x(3)-x(2))/T1; x(4); E_DOT*(kr+Tr/T3)+e*kr/T3-x(4)/T3; e^2];
    end

In the above code I need to replace "E_DOT" with the derivative of e. How can I do it?

T1, T2, kr and Tr are constants.

Answer 1

[David Goodmanson]

Hi Pawel,

you have

e = -x(1) + 1;

so

de/dt = d/dt(-x(1) + 1) = -dx(1)/dt

but

dx(1)/dt = (x(2)-x(1))/T2

so you can replace E_DOT with

-(x(2)-x(1))/T2