Hello,
Given a system of differential equations as:
C*V = O; where O is a null matrix and C is a 3X3 matrix as follows:
Row 1: [rho*(alpha*I+omega*U*I), rho*U', alpha*I]
Row 2: [0, rho*(alpha*I+omega*U*I), d/dy]
Row 3: [alpha*I, d/dy, M^2*(alpha*I+omega*U*I)]
The prime in Row 1 denotes differentiation with respect to y, and I is the unit imaginary number, d/dy is a differential operator. The vector V is given by:
V = [u; v; w];
How do I use Maple to do a Gauss Elimination on the coefficient matrix which will give me separate equations for each of u, v and w. Or to be more specific, how do I represent the differential operator d/dy in a matrix

The attached Maple10 worksheet solves a system of differential equations. A plot of the solutions y1(t) (red curve) and y2(t) (green curve) appears below. Download 2353_fsolve-avoid.mws

View file details As a check, I want to use fsolve and the "avoid" option to find both times at which y1 has the same value as when y1=y2, but I'm having trouble. I would appreciate any advice on how I can get the "avoid" option to work for me. fsolve finds the earlier time easily enough (t=.9036852930e-1), but when I use the "avoid" option (highlighted statement below) to find the later time (t=.5225499740), I get the error "Error, (in fsolve) avoid = {.9036852930e-1} is an invalid option." The code is appended below. Thanks. Glenn ======== ` > restart; > with(plots): > sys:= Diff(y1(t),t)=-3*y1(t) + 2*y2(t), Diff(y2(t),t)=y1(t)-3*y2(t); > ic := y1(0)=1, y2(0)=5; `

` d d sys := -- y1(t) = -3 y1(t) + 2 y2(t), -- y2(t) = y1(t) - 3 y2(t) dt dt `

` ic := y1(0) = 1, y2(0) = 5 `

` > odesol:=dsolve({sys,ic},{y1(t),y2(t)},type=numeric,output=listprocedure); odesol := [t = (proc(t) ... end proc), y1(t) = (proc(t) ... end proc), y2(t) = (proc(t) ... end proc)] `

` > Y1:=eval(y1(t),odesol); Y2:=eval(y2(t),odesol); `

Y1 := proc(t) ... end proc Y2 := proc(t) ... end proc ` > Teq:=fsolve('Y1'(t)='Y2'(t),t); `

Teq := 0.5225499740 ` > Yeq:=Y1(Teq); Y2(Teq); `

Yeq := 1.45974175440983366 1.45974175447049736 ` > T1:=fsolve('Y1'(t)=Yeq); T2:=fsolve('Y2'(t)=Yeq); `

T1 := 0.09036852930 T2 := 0.5225499740 ` `** > fsolve('Y1'(t)=Yeq, t, avoid={T1}); ** fsolve('Y1'(t)=Yeq, t=T2);

Error, (in fsolve) avoid = {.9036852930e-1} is an invalid option 0.5225499740 ` > Y1(%); `

1.45974175440983366 ` > plot({Y1(t),Y2(t)},t=0..3); `

I am relatively new to Maple, and have been attmpting to solve this for the last few days, and if somebody would be able to help me out that would be great. I am attempting to make the list of following equations smooth (supposed to be for a roller coaster):
u(x)=.8x (where x is less than 0)
g(x)=kx^3 + lx^2 + mx + n (where is is greater than or equal to 0 but less than 10)
f(x)=ax^2 + bx + c (where x is greater than or equal to 10 but less than or equal to 90)
h(x)=px^3 + qx^2 + rx + s (where x is less than 90 but greater than or equal to 100)
t(x)=-1.6x + 120 (where x is greater than 100)

I am trying to use Optimization[LSSolve] to fit the solution to a differential equations to data. I can solve my problem using Matlab, but I'd like to be able to use Maple as well. This is Maple 10. The proc is not getting the values of the parameters.
> data := [[0,95], [11,425], [22, 928], [33,1358], [44,1589], [56,1683], [67,1724]]:
> try2 := proc(K,alpha,r,IC)
local DE1,R; print(K,alpha,r,IC): # for debugging
DE1:=diff(y(t),t)=r/alpha*y(t)*(1-(y(t)/K)^alpha);
R:=dsolve({DE1,y(0)=IC},numeric);
map((d) -> rhs(R(d[1])[2])-d[2],data):
end:
> sol2 := Optimization[LSSolve](try2(K,alpha,r,IC), initialpoint = {r=.09, K=1750, IC=95, alpha=.3});

Hi,
I have a ‘slight’ problem (you will probably recognize it Joe! :-) ).
It concerns the values of Tau, omega in my worksheet (see below). If I set Tau=0.7, omega=0.7*m*Eta everything is rosy, and works fine. If I start tweaking these values (which I have to) things go a bit pair shaped.
I either get an error message after the first call to dsolve (e.g. when tau=0.5, omega=0.7*m*Eta) :
*"Error, (in dsolve/numeric/checksing) ode system has a removable singularity at r=1. Initial data is restricted to {Phi(r) = .20650095602297*diff(Phi(r),r)+.82088920025557e-1*I*diff(Phi(r),r)}"*

I don't know how much interest this has for people on this forum, but I have just discovered (I think) a difference in how M10 and M11 handle differential equations. I just received M11 late last week, and when I tried to run in M11 a worksheet I had developed in M10 I got an error. It had to do with the fact that M10 gave me 2 solutions to a DE, whereas M11 gave me one. The first solution which M10 gave me was r(theta) = 0. M11 skipped this trivial solution. Arguably this is a better way to go, but it can cause problems for older worksheets, as it did on mine, where my next line tried to parse the second solution of the previous line. I have uploaded a file which illustrates this. Is it possible that there is some setting I could change in M11 to make it give me the same set of solutions as M10 gives?

Hi.
>sol2:=dsolve(
{diff(c(x),x,x)=c(x) , c(0)=5, int(c(x),x=0..1)=3 },c(x));
Error, (in PDEtools/sdsolve) the input system cannot contain equations in the arbitrary parameters alone; found equation: _F1[x]-3
this is a DE of second order, so it requires two conditions to find the constants.. I wanted to give one of the conditions in the form of an integral, but i get the error above.
Any idea why?
thanks

hi guys!
Alright... I have a system of equations in the form of:
y=ux^[v+w*ln(x)]
So this is what I do:
1.Define the function:
h := -> u*x^(v+w*ln(x))
2.Next, I have to tell maple some solutions to this equation:
eqns1 := {h(.6) = 13, h(5) = 120, h(11) = 1000}
3.tell maple to solve:
solve(eqns1, {v, u, w})
But I get:
Warning, solutions may have been lost
and I get no solutions.
What is the problem with what I have input?
Thanks a lot guys!

I got the eigenvalues of the Jacobian matrix of a nonlinear time variant system. One of them is like:
0.5000000000e-2-0.2500000000e-2*y+0.5000000000e-2*x+0.2500000000e-2*sqrt(36.-12.*y-24.*x+y^2-4.*x*y+4.*x^2)
Now I'd like to make x and y still vary with time, i.e.
0.5000000000e-2-0.2500000000e-2*y(t)+0.5000000000e-2*x(t)+0.2500000000e-2*sqrt(36.-12.*y-24.*x(t)+y(t)^2-4.*x(t)*y(t)+4.*x(t)^2)
x(t) and y(t) bear a relation by differential equations.
Any ideas on how I implement this?
Thanks a lot!

February 27 2007
Jinny 8
Hi everyone,
Could you please have a look at my maple file. Im trying to solve a set of 4 differential equations but maple takes ages to solve and doesnot give the answer at the end either. The reason can be that the equations have to high power.
Do you know any other dsolve method I can use or anything I can do to fix this problem?
Thank you very much!
Jinny

View 3868_Pressure drop 2.mw on MapleNet or

Download
Ok, another of my "how do you do this" questions:
In solving a an equations such as:
y''-4*y'+5*y = 0
I would like to show the roots; is there a function that will just pull the roots from the equation as written or do I have to write the equation like:
m^2 + 4*m + 5 = 0
and use:
solve(m^2+4*m+5);
Thanks...

People on this forum have been unbelievably helpful.
I am trying to write some worksheets to help flatten the learning curve for folks who are new to MAPLE. Trouble is, being not far from the newbie stage myself, I may very well be making significant mistakes about the capabilities of MAPLE and thus teaching people cumbersome and inefficient ways of doing things. With that in mind, if anyone has the time to critique the following, I would be most appreciative.

I am having the hardest time plotting the qualitative behavior of the solutions of these differntial equations. I keep getting Error, (in plots/animate) no non-zero vectors found. If someone could walk me through plotting these equations, it would be greatly appreciated.
Equation1: dx/dt=x^2, x(0)=1, 0≤t<>

February 21 2007
derio 40
My goal is to obtain a formula F:= x -> fa(x)*c1_1(x)+ fb(x)*c1_2(x)+fc(x)*c2_1(x)+... where every ci_j(x) is a function of x. fa, fb, fc are known functions of x. I do not need to have it printed, I just need it to return a numerical value for every value of x I throw in.
I have obtained the solutions of ci_j's in the form
Sol[1]:=[c1_1=f11(x), c1_2=f12(x), c1_3=f13(x), ...], N1 terms
Sol[2]:=[c2_1=f21(x,c1_j’), c2_2=f22(x,c1_j’), c2_3=f23(x,c1_j’), ...], N2 terms
Sol[3]:=[c3_1=f31(x,c1_j’,c2_j’), c3_2=f32(x,c1_j’,c2_j’), c3_3=f33(x,c1_j’,c2_j’), ...], N3 terms
Sol[4]:=[c4_1=f41(x,c1_j’,c2_j’,c3_j’), c4_2=f42(x,c1_j’,c2_j’,c3_j’), c4_3=f43(x,c1_j’,c2_j’,c3_j’), ...], N4 terms