MaplePrimes - Questions and Posts tagged with differential

Non-autonomous system of DE to autonomous one

johnnyV — Mon, 17 Jun 2013 18:46:32 Z

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

differential equation solutions

Ratch — Fri, 03 May 2013 21:38:42 Z

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...

terms identification

Bendesarts — Sun, 24 Mar 2013 12:01:55 Z

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...

How to split or directly plot a system of solved differential equations

OffshoreEngineer — Tue, 19 Mar 2013 13:43:48 Z

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...

How to interpolate roots for a curve expressed in numerical arrays

mapleq2013 — Fri, 15 Feb 2013 21:40:09 Z

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!

Solving system of differential equations with bound on solutions

mapleq2013 — Thu, 14 Feb 2013 21:43:40 Z

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!

Simplifying a vector expression with composite functions

PlpPlp — Wed, 13 Feb 2013 11:57:48 Z

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:

= 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...

Warning, expecting Range variable k blablabla... while trying to plot

digerdiga — Thu, 31 Jan 2013 17:23:35 Z

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...

Differential equations solving and plotting

gdog — Wed, 30 Jan 2013 13:11:32 Z

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...

Steady state concentration

call_me_jeremy — Wed, 30 Jan 2013 10:43:32 Z

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...

Reducing order of system of differential equations

georgeee — Tue, 29 Jan 2013 23:27:40 Z

Dear all, I am new here, so I am sorry in advance if I make some mistakes. The problem here is how to transform

system of 2 differential equations 4th order to the system of 4 diff equations second order, or how to reduce system of 2 equations 4th order on two equations second order with vanishing solutions which I choose because they are big. Here is example

Solving and then plotting differential equations

gdog — Fri, 25 Jan 2013 20:04:25 Z

Hi I have three differential equations:

u := diff(P(t), t) = -7*10^(-8)*P(t)*t/(P(t)*t+R(t))^(1/2),

diff(R(t), t) = 7*10^(-8)*t^2*P(t)/(P(t)*t+R(t))^(1/2)+600*(Z(t)^2-10^5*t^3*(1/(1.15*10^12))^(2/3)*e^(-1.15*10^12))/(t*(P(t)*t+R(t))^(1/2)),

diff(Z(t), t) = -4*10^5*(Z(t)^2-10^5*t^3*(1/(1.15*10^12))^(2/3)*e^(-1.15*10^12))/(t^2*(P(t)*t+R(t))^(1/2))

and i want to solve them with initial conditions:

initial := R(0) = 0, Z(0) = 0, P(0) = P;

Coupled differential equations

paul7dxb — Tue, 22 Jan 2013 15:06:04 Z

I have been told that dsolve solves a second order differential equation by making two coupled first order equations.

Could someone please explain to me the reason that this is done?

how to stop maple from evaluating my solution and pass as string

vineetloya — Wed, 12 Dec 2012 18:52:17 Z

Hello,

I am working on a Maple project and it require me to pass a differential equation in a specific order like

x'=y & y'=x^2.(It is differentaiting w.r.t 't'(say))

However when I convert the equation into string it converts something as

diff(x(t),t)=y(t) & diff(y(t),t)=x(t)^2

Is there any way to stop maple from evaluating into maple/math format?

Is there any way to pass an equation without changing it's existing form?...

How do I input multiple solutions to an equation when using dsolve?

Professor_Pie — Thu, 22 Nov 2012 22:37:59 Z

Hello!

I am trying to solve the differential equation:

for ,