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

Dear Sir:
I try to solve a set of simultaneous equations.
But, it is not easy to get a solution by using
MAPLE package.
restart;
eq1:=P-2*P*cos(w*t[2])+(P+1)*cos(w*t[3])=0;
eq2:=-2*P*sin(w*t[2])+(P+1)*sin(w*t[3])=0;
_EnvAllSolutions:=true: _EnvExplicit:=true:
solve({eq1,eq2},{t[2],t[3]});
But, MAPLE does not give me what I want.
I expect that the solution should be in
the following way:
t[2]=(1/w)*arccos((4*P^2-2*P-1)/(4*P^2));
t[3]=(1/w)*arccos((2*P^2-2*P-1)/(2*P^2+2*P));
where w and P are positive constants.
Could you help me to get the solution?
Thanks

February 16 2007
Nasos 84
Hi,
I have three equations Y=f(t) with each equation corresponding to a probability as shown below.
Y1=f(t) with probability of 0.05%
Y2=f(t) with probability of 5% and
Y3=f(t) with probability of 50%
If we assume that these probabilities belong to a normal distribution how can I work out the equations for 99.95% and 95%probability.In other words I would like to mirror Y1 and Y2.
The idea is to plot all the equations of 0.05%,5%,50%,95% and 99.95% probability in the same plot and create a 3D surface where the axis will be Y,t and P(probability) or even better generate the equation of P=f(Y,t) that will describe this surface.

how do I solve differential equations with maple V?

When I use PDEtools in Maple10 to get subscript notation of derivatives it works for equations that are assigned to another variable name. It does not work for equations that are referred to only by their Maple10-generated equation numbers. The sample case below shows the problem. It is an edited Maple-text version. I tried uploading the file, but neither Live Worksheet or HTML copy correctly display. Live Worksheet apparently doesn't access PDEtools, and the HTML copy can't handle equation number references. I can supply the test file to any one who wants it.
------------------------------------------------------------------------------

Iam a Student in the faculty of engineering Petroleum department.
Iam Studying Oil Reservoir Simulation which havs many models.
Iam Studying the mathematical modeling of those reservoirs.
In this modeling we use PDEs to model that reservoir behaviour for years
we devide the reservoir into grid blocks each of its special dimensions and parameters
so for each grid block there are 3 phases which are oil, water, and gas equation (one for each phase of them)(Matrix Dimension = No. of phases * No. of grid blocks) in addition to the other parameters
there are some elements of the PDEs which is function in more than one parameter

Hello all!
I need to solve multivariate polynomial equations modulo a positive integer 'm', where 'm' is not prime. Which function would be best?
Also, how do I include constraints to the above set of equations? For instance, if I need to solve for 'x' and 'y' such that
f(x,y) = 0 mod m
g(x,y) = 0 mod m
f != g mod m
Any help would be great!!

hi, I have a big problem with my project. I need a help with solving and plotting three differential equations but I can´t do it. The project is about lotka-volterra system with three species, 2 predators and 1 prey with no competition between predators. Thanks for a help.
eqPrey := diff(X(t), t) = alpha1*X(t)*(1-X(t)/K) - beta1*X(t)*Y(t)-gamma*Y(t)*Z(t);
eqPred1 := diff(Y(t), t) = -alpha2*Y(t) + beta2*X(t)*Y(t);
eqPred2 := diff(Z(t), t) = -alpha3*Z(t) + beta3*Z(t)*Y(t);

I got this problem from my proffesor :
*Provide a MAPLE procedure which plots ANY curve C given by a pair
of Cartesian implicit equations { f(x,y)=0 & g(x,y)=0 }, without
plotting as well the two surfaces ( f=0 and respectively g=0 ),
which provide C by their intersection (just the curve C has to
appear as output). Do NOT attempt to parametrize the curve; use
the MAPLE plotting functions for Cartesian plots.
Example: C: { x^2+y^2+z^2-1=0 and z=0 } is a circle in the xOy
plane;
plot the circle, but not the sphere or the plane which provide C.
*

hey :)
i have a set of equations on the form in the example below. i included my attempt at a solution which, as you might suspect, does not give me the answer on the form i want.
what i want is to solve this assuming that the coefficients for each term in the polynomial of u and v sould be equal.
eq1 := a1*u^2 + (a4 + 3 + 2*a6)*u*v + a3*v^2 + (a1 + a2 + a6)*u + a5*v + a6 = 5*u^2 + 7*v;
solve(eq1, {a1,a2,a3,a4,a5,a6});
this example would for example have the solutions:
a1 = 5
a2 = -5
a3 = 0
a4 = -3
a5 = 7
a6 = 0
but if you type the code ive written into maple, youll see thats not what i get at all :)

I wonder if someone could help explain to me how to use Matrix equations. Suppose A is a 3x3 matrix of constants, b a 3 vector of variables (x,y,z) and c a 3 vector of constants. The equation A.b = c is really 3 equations in x y z. Is it possible to extract those equations from the matrix equation A.b = c? I explain my question more clearly in the uploaded worksheet.
Thanks
The link can be found in the

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Hello,
I'm trying to export a worksheet in LaTeX format. It gives me a .tex file which requires a package maplestd2e.sty (not maple2e.sty) which I don't have. I found a file called maple2e.sty at http://www.maplesoft.com/support/downloads/latex_patch.aspx and it works up to a point. Firstly I had to change the output tex file to require package maple2e.sty and more importantly it has equations running off of the edge of the page.
Please help,
Regards,
A. Carmichael