Has Maple 11 changed the way you do mathematics?
For me, it has.
For me, Maple used to be a “mechanized mathematical assistant”. That is, when I was doing something mathematical, I would do it at my desk, with Maple on a computer beside me, to assist with some of the calculations. I used many sheets of paper; the papers were messy and disorganized. I would scribble equations, scratch out mistakes or recopy the good parts onto another sheet, have sub-results strewn about haphazardly, etc.
With Maple 11, things are different. Now I do mathematics almost entirely within Maple. Now I keep everything in a document. I type formulae with 2D input, which looks much like how I would write things on paper, except neater. Graphics are interwoven with the formulae (and can be scribbled on). Mistakes are erased within the document. Sub-results are nicely put into collapsible subsections. The organization can, and of course does, change as I figure things out.

When I enter solve(x^4-x^3+1) I get 4 RootOf place holder solutions. For example RootOf(_Z^4-_Z^3+1, index = 1). This is very frustrating because I'm trying to obtain answers not place holders, and I cannot figure out how to make Maple solve the problem. Is Maple perhaps trying to tell me that it cannot solve the problem? If not, how do I force Maple to return answers instead of place holders, on this and similiar problems? Just as there is the quadratic equation for obtaining solutions to second degree equations, I understand that there are standard equations for solving cubics and quartics so I would be surprized if maple cannot solve x^4-x^3+1 symbolicly.

My class was given this question as a final homework but we can't figure out how to solve it. We have talked to the professor on multiple occasions but he will not provide any help. If anyone knows how to solve this using maple, please help. The question is below...
solve x(t) = Ax(t)+B where
B=[1
-1]
A=[-1 0
1 2]
and x(0) = (1 0)
Sorry for the matrix formatting but, I don't know how to use the math equations here.

I have two equations with 3 variables(or perhaps n equations with n+1 variables)
eq1:=0=c1*A1+c2*B1+c3*C1;
eq2:=0=c4*A1+c5*B1+c6*C1;
I can solve by e.g.
solve({eq1,eq2},{A1,B1})
or any other combination of two of the variables.
But if I follow the above by
solve({eq1,eq2},{B1,C1})
I get then get an error. How do I find C1 as a function of A1?
There must surely be a very way simple to do this.
Did check the help pages but must have missed it if it is there.

There are two equations f'''+1/2*f*f''=0 and g'''+1/2*g*g''=0
boundary value
f(0)=0
g(0)=0
f'(0)=g'(0)(is not zero)
f''(0)=g''(0)
f'(4)=1
g'(-4)=0.5
Because of two coupled boundary value (f'(0)=g'(0, f''(0)=g''(0)), it
is difficult to solve.
Could you tell me how to solve this equation using matlab?
Thanks.

I am trying to create a plot for two differential equations but I'm not getting any graphs with the commands below. I'm not sure what's causing the problem and I've tried everything I can think of. Please help if you can.
a := 2*ln(2)
b := 1/5*ln(2)
dose := proc (t) options operator, arrow; sum(2*Heaviside(t-6*n)-2*Heaviside(t-6*n-1/2), n = 0 .. 10) end proc
J:=DEplot([diff(x(t), t) = dose(t)-a*x, diff(y(t), t) = a*x-b*y], [x, y], 0 .. 50, {[0, 0, 0]}, stepsize = .5, scene = ([t, x]))
K:=DEplot([diff(x(t), t) = dose(t)-a*x, diff(y(t), t) = a*x-b*y], [x, y], 0 .. 50, {[0, 0, 0]}, stepsize = .5, scene = ([t, y]))

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!