Here is a system to ODE i am trying to solve:

w(t) = x(t) + x'(t) + w(t-a)

x''(t) = x'(t) + w(t)

How can i solve this kind of ODE with delay in time?

aks.

I am currently studying the phase portrait a differential equation: diff(y(t), t, t) = -piecewise((diff(y(t), t))*y(t) <><> 0 <><><> Initial conditions are: y(0) = 1; , diff(y(0), t) = 0; The phase portrait plots diff(y(t),t) with respect to y(t). I achieved the phase portrait using Simulink; with a few gain blocks, a switch and a X-Y scope, easily enough. When i was done, i wondered if i could analyze the equation with a more mathematical approach. I decided to try and plot the phase portrait using Maple 11. I have tried various commands to solve the differential equation with Maple 11 but so far i have confused myself.

Hi all, Here are my questions: 1) How do i perform small-angle approximation (linearization) on a nonlinear DE using Maple. This is necessary to create a state-space representation of the DEs. By small-angle approximation i mean that: sin(theta(t))=theta(t) cos(theta(t))=1 theta(t)^2 = 0 theta(t)*alpha(t)=0 and so on.... I tried using manual substitution using the "subs" command. It is not a very feasible method. I have tried "dsolve" command. Not what i want since i only want to linearize the DEs and not solve for a particular angle. 2) My second question is regarding defining outputs of the "DiffEquation" command. Usually it will go: