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how to get kalman form...

October 18 2013 Ex 70

The goal is to get Kalman Form

https://docs.google.com/file/d/0Bxs_ao6uuBDUT25BeVhtWjZwRUU/edit?usp=sharing

https://docs.google.com/file/d/0Bxs_ao6uuBDUVXU5dXh6Rl9zUUU/edit?usp=sharing

 

I am doing the example in page 707 of Partial Differential control theory Volume 2 by J.F.

 

when using Robertz Daniel's Ore and Involutive packages

 

with(Involutive):

with(OreModules):

Alg := DefineOreAlgebra(diff=[D,t...

Diff(x1(t),t) - x2(t) = 0;

Diff(x2(t),t) - x3(t) = 0;

Diff(x3(t),t) +3*x3(t) + 4*x2(t) + x1(t) = 2*Diff(u(t),t$2) + 5*Diff(u(t),t) + 7*u(t);

 

multiply above system by test functions -lambda1(t),-lambda2(t),-lambda3(t) and integrate by part

in order to find adjoint operator in the form

 

x1 -> Diff(lambda1(t),t) - lambda3(t) = miu1(t)

x2 -> Diff(lambda2(t),t) + lambda1(t) - 4*lambda3(t) = miu2(t)

Can maple use a Differential Operator somehow in the following sense?

Instead of expanding (D-p)^n where p is a constant and D the differential operator and n an integer and then in each term writing D^n(f) for some function can I just leave the expression as it is like

(D-p)^n and acting on everything on the right?

Hi every body

I want to solve a differential equation y'(t) = sqrt((f-1)/(t^f-t)) and get an answer in terms of ordinary function.is it possible. thanks 

Hi,

I'm searching for the third differential equation that will transform the following two equations non-autonomous system into a three equations autonomous one:

diff(x(t),t)=-x(t)+2*(m*t+n)*y(t)-2*k*(m*t+n)2

diff(y(t),t)=-y(t)+k*m-(m*t+n)*((x(t)/2)-1)

 

diff(z(t),t)= ...

 

Regards,

Johnny

     Many times when I use dsolve to find the solution of an equation like x-y/y' = y , I get a term involving the LambertW function.  However, the equation has homogeneous coefficients for dx and dy, so it can easily be solved by substituting y=u*x and separating the variables.  The closed form solution of the above is x+y*ln(y)+c*y = 0 , but I cannot get that answer from Maple.  Is there...

Hello, 
I'd like to identify terms before the differential terms (theta(t), diff(theta(t),t) ...)

The following code with coeff function works for  diff(theta(t), t, t)) but not for diff(theta(t), t)
Here the code :
eq1pp := R(t) = -(-sin(theta[0]+phi)*Isup-sin(theta[0]+phi)*L[fixe]^2*M[fixe]-sin(theta[0]+phi)*L[r]^2*M[r]-sin(theta[0]+phi)*L[sup]^2*M[sup]+cos(theta[0]+phi)*a*sin(phi)*L[fixe]*M[fixe]+cos(theta[0...

Hi all,

I am new to Maple and I have (possibly a simple) question. I'm solving 2 coupled differential equation, it all goes well, until I want to plot them.

I have the output in the following form:

sol = {w1(x) = [ -a*x^4+b*x^3-c*x]}, {w2(x) = [-d*x^4+e*x^3-f*x^2+gx-h]}

My goal is now to plot the solution in 1 figure with w1(x) between x=0..100000 and w2(x) between x=100000..150000

I have searched on the web for a way to get the formula's of w1(x...

I'm solving a system of ordinary differential equations numerically, I used the dsolve(system,numeric) to do it. I have also plotted the solutions. Now I want to know where does this solution cross zero and use this value for later computations, is there a way to do it? 

This question is, as I think, equivalent to how to find the roots for a curve expressed in numerical arrays.

Thank you!

I know how to solve system of differential equations numerically, but now I want to know how to set a bound on the solutions. 

For example, if my system of DE is like this:   dx/dt = x+y   dy/dt = x-y    , solve x and y in t. 

I can solve this without any restriction on x and y, now I need to know how to bound x and y, e.g. x can only fall in the interval [0,1]

 

Thank you very much!

Hi all,


I must confess I'm a perfect novice in Maple as I'm used to work with Matlab. I have a 3d differential equation, namely:


dM/dt+gamma*mu[0]*`&x`(M, H[eff])-G/(gamma*M^2) *`&x`(M, dM/dt)= 0

The components of M should be of the form M_{i0} + dM_i(t) where M_{i0} is a constant and dM_i(t) a function of t, i = 1, 2, 3. And...

I dont know what to do any further...

I have some function containing HeunG as a function

it is of the following form

f(k)=argument(functions containing HeunG) - ln(2)*k

now plotting this works...

But when differentiating with respect to k and then plotting it gives me the following message:

Warning, expecting only range variable k in expression (I*((1/2)^(1/2*I*k))^2*HeunG(3,-9/2+3/4*I*k-3/4*k^2,-1+1/2*I*k,-1/2+1/2*I*k,1/2,1+I*k,1/2...

Hi I have the differential equations:

X := diff(F(t), t$2)+(10+8*sin(m*t)/(m*t))*F(t) = 0

I know that if it were X := diff(F(t), t$2)+(W)*F(t) = 0, where W was a constant, then the solution would be the standard WKB sol, but with a time varying function in front this solution is no longer valid.

 

I know this can be done and would like some help in plotting F(t) against t and i sholud look an oscialltig curve where when sin(mt)=0 it...

Hi,

I'm new in Maple and i've a project to do. I've to find at what time is 90% of the steady-state concentration of C achieved. And the eq is 

z'=k(1/2-z)(1/3-z), where k=0.3. 

So i had worked in Mathematica before and i know that it would look something like that in there: 

eqn1 = 0 == k (1/2 - z[t]) (1/3 - z[t])

DSolve[Evaluate[{eqn1}], z[t]].

But i have no idea how to find this 90%. I hope that someone will...

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