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Any suggestions (or perhaps related examples?) illustrating how I might numerically solve for f(t) in the following non-linear integral equation?  In Fortran, I would start with a guess f(t)=T0, and then search in the neighborhood for a minimum (in the error), but I am not familiar with numerical searches and methods in Maple.  Thank you for any suggestions or leads.

(a,b,... etc are all real)


T__0 := 298.

`ΔT` := 25.

0 < beta and beta <= 1

``

f*t = T[0]+`&Delta;T`*[1-exp(-a(int(exp(-b/f(y)), y = y[1] .. t))^beta)]

NULL


Download Integraleqn.mw

 

 

 

How to find (i. e. to evaluate) the positive root of the polynomial equation

mul(x+j, j = 0 .. 2015)=1?

The command

RootFinding:-NextZero(x-> mul(x+j, j = 0 .. 2015)-1 , 0);

outputs

                              FAIL
The same with Digits:=100.

I'm struggling to get my head around using Z-transforms in maple

What steps would I have to take to get

a)

Find y[n], the inverse Z-transform of

z/(z-2) 5z/(z-5)^2

 This is using the invztrans command but no solution is being given

b)

by evaluating y[n]/q[n], when

q[n]=Σ{k=0}2^n-k k5^k

show that y[n]=q[n]

 (With this I believe I should be using the ztranz command?)

hi, the equations read as 

eq:=[2*x-0.2e-1*y-2.04*sqrt(-v^2+1)*v, 2*y-0.2e-1*x-2.16*sqrt(-u^2+1)*u, 2*u+2.16*u^2*y/sqrt(-u^2+1)-2.16*sqrt(-u^2+1)*y, 2*v+2.04*v^2*x/sqrt(-v^2+1)-2.04*sqrt(-v^2+1)*x] ;

i do as follows using DirectSearch package v.2

i find the solutions not the same,some time the results not much difference,but another,sols1 have one solution,sols2 have three solutions.in some time,some solutions are lost,the result show  me  random.may i have run the command serveral times? regards.

Can I use Maple to solve equation like |a-b|+\sqrt{2b+c}+c^2-c+1/4=0 for a,b,c?

 

a,b,c are real numbers and I need to solve it in real domain.

Hey,

I've been trying to divide an equation into matrixes, with not a lot of luck.

Simple example:

A=2b remade into [A]=[2]*[b]

This is a basic overview of the problem, i need it to work with bigger matrixes.

Thank you in advance.

Hello!
Please help solve this equation!

restart;

Dd:=4.9*10^(-10):
n:=4.5:
m:=3.5:
ny:=20:
B:=1.47*10^(-11):
H1:=70:
H2:=20:
H:=100:
b1:=40:
b2:=80:
delt_y:=H/ny:
A_max:=b1*H1+b2*H2+10*b1:
M:=1000:




b:=y->piecewise(`and`(y>=0,y<=H1),b1,`and`(y>H1,y<H1+H2),b2,`and`(y>=H1+H2,y<=H),b1):
y:=0: eq:=0:

for j from 1 to ny do
y:=(j-1)*delt_y+delt_y/2;

eq:=evalf(eq+b(y)*sign(y-y0)*abs((y-y0))^(1/n)*delt_y);
end do;


#eq=0, y0-?
sol1:=fsolve({eq=0},{y0});

Hi all,

 

It's been a while since I have used Maple. To be honest I haven't used it for over six years.

 

I am trying to solve simple differential equations, however I have many issues.

 

I am trying to simulate what author of this paper did 06421188.pdf

 

My file looks like this (Pendulum.mw)

 

Can someone help me to simulate this system? I simply can't remember how to do it.

 

Cheers,

Bart

Hello there

I'm quite an amature so please don't judge.  I'm trying to use fsolve to solve a system of non-linear equations but Maple is just "spitting" on me the equations with no intention to solve them:

> delta5 := P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+zeq^2)*(sqrt(x^2+zeq^2)*x))+x*zeq/sqrt(x^2+zeq^2)^3)/(2*Pi*E5);
print(`output redirected...`); # input placeholder
> shrinkage := P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+Zb^2)*(sqrt(x^2+Zb^2)*x))+x*Zb/sqrt(x^2+Zb^2)^3)/(2*Pi*E5)-P*(1+mu5)*((1-2*mu5)*x/(sqrt(x^2+Za^2)*(sqrt(x^2+Za^2)*x))+x*Za/sqrt(x^2+Za^2)^3)/(2*Pi*E5);
> eq10 := subs(x = 1800, delta5)+subs(x = 1800, Zb = z2, Za = z1, shrinkage)+subs(x = 1800, Zb = z3, Za = z2, shrinkage)+subs(x = 1800, Zb = z4, Za = z3, shrinkage)+subs(x = 1800, Zb = z5, Za = z4, shrinkage) = 36.7*10^(-3);
print(`output redirected...`); # input placeholder
> eq9 := subs(x = 1500, delta5)+subs(x = 1500, Zb = z2, Za = z1, shrinkage)+subs(x = 1500, Zb = z3, Za = z2, shrinkage)+subs(x = 1500, Zb = z4, Za = z3, shrinkage)+subs(x = 1500, Zb = z5, Za = z4, shrinkage) = 47.2*10^(-3);
print(`output redirected...`); # input placeholder
> eq8 := subs(x = 1200, delta5)+subs(x = 1200, Zb = z2, Za = z1, shrinkage)+subs(x = 1200, Zb = z3, Za = z2, shrinkage)+subs(x = 1200, Zb = z4, Za = z3, shrinkage)+subs(x = 1200, Zb = z5, Za = z4, shrinkage) = 63.8*10^(-3);
> eq7 := subs(x = 900, delta5)+subs(x = 900, Zb = z2, Za = z1, shrinkage)+subs(x = 900, Zb = z3, Za = z2, shrinkage)+subs(x = 900, Zb = z4, Za = z3, shrinkage)+subs(x = 900, Zb = z5, Za = z4, shrinkage) = 91.1*10^(-3);
print(`output redirected...`); # input placeholder
> eq6 := subs(x = 600, delta5)+subs(x = 600, Zb = z2, Za = z1, shrinkage)+subs(x = 600, Zb = z3, Za = z2, shrinkage)+subs(x = 600, Zb = z4, Za = z3, shrinkage)+subs(x = 600, Zb = z5, Za = z4, shrinkage) = 137.9*10^(-3);
> eq5 := subs(x = 450, delta5)+subs(x = 450, Zb = z2, Za = z1, shrinkage)+subs(x = 450, Zb = z3, Za = z2, shrinkage)+subs(x = 450, Zb = z4, Za = z3, shrinkage)+subs(x = 450, Zb = z5, Za = z4, shrinkage) = 175.2*10^(-3);
> eq4 := subs(x = 300, delta5)+subs(x = 300, Zb = z2, Za = z1, shrinkage)+subs(x = 300, Zb = z3, Za = z2, shrinkage)+subs(x = 300, Zb = z4, Za = z3, shrinkage)+subs(x = 300, Zb = z5, Za = z4, shrinkage) = 230.9*10^(-3);
print(`output redirected...`); # input placeholder
> sys := {eq10, eq5, eq6, eq7, eq8, eq9};
print(`output redirected...`); # input placeholder
> fsolve(sys, {E1 = 1000 .. 2000, E2 = 0 .. 2000, E3 = 0 .. 2000, E4 = 0 .. 2000, E5 = 0 .. 2000, h4 = 100 .. 400});

and this is what Maple gives after the fsolve

 

fsolve({(3937.500000*(.2/(202500+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(450*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(202500+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.3888888889e-2/E5+(3937.500000*(.2/(202500+(650+h4)^2)+(450*(650+h4))/(202500+(650+h4)^2)^(3/2)))/E5 = .1752000000, (3937.500000*(.2/(360000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(600*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(360000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.2187500000e-2/E5+(3937.500000*(.2/(360000+(650+h4)^2)+(600*(650+h4))/(360000+(650+h4)^2)^(3/2)))/E5 = .1379000000, (3937.500000*(.2/(810000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(900*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(810000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.9722222220e-3/E5+(3937.500000*(.2/(810000+(650+h4)^2)+(900*(650+h4))/(810000+(650+h4)^2)^(3/2)))/E5 = 0.9110000000e-1, (3937.500000*(.2/(1440000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1200*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(1440000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.5468750000e-3/E5+(3937.500000*(.2/(1440000+(650+h4)^2)+(1200*(650+h4))/(1440000+(650+h4)^2)^(3/2)))/E5 = 0.6380000000e-1, (3937.500000*(.2/(2250000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1500*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(2250000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.3500000000e-3/E5+(3937.500000*(.2/(2250000+(650+h4)^2)+(1500*(650+h4))/(2250000+(650+h4)^2)^(3/2)))/E5 = 0.4720000000e-1, (3937.500000*(.2/(3240000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)+(1800*(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3)))/(3240000+(146.0507832*(E1/E5)^(1/3)+197.1094212*(E2/E5)^(1/3)+295.6641318*(E3/E5)^(1/3)+1.*h4*(E4/E5)^(1/3))^2)^(3/2)))/E5-0.2430555555e-3/E5+(3937.500000*(.2/(3240000+(650+h4)^2)+(1800*(650+h4))/(3240000+(650+h4)^2)^(3/2)))/E5 = 0.3670000000e-1}, {E1, E2, E3, E4, E5, h4}, {E1 = 1000 .. 2000, E2 = 0 .. 2000, E3 = 0 .. 2000, E4 = 0 .. 2000, E5 = 0 .. 2000, h4 = 100 .. 400})

Is it possible to plot the equation 1=x^2+(y-1)^2 within Maple without rewriting it into a function or something like that? I can see that it is an easy to plot circle, but I just wonder whether it is possible.

Hi, I am completely new to Maple, and I need to use it to optimize my equations in order to make my PLC codes more compressed. I am calculating forward kinematics with the Denavit-Hartenberg method and as such I get long expressions. After a lot of google'ing and frustration, I thought I'd ask here in the hope that one of you might be able to assist me.

I have the following equations;

X := L10*cos(q5) - L16*(sin(q10)*(sin(q5)*sin(q8) - cos(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) - cos(q10)*(sin(q9)*(cos(q8)*sin(q5) + sin(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) + cos(q9)*(cos(q5)*cos(q6)*sin(q7) + cos(q5)*cos(q7)*sin(q6)))) - d2*(cos(q10)*(sin(q5)*sin(q8) - cos(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) + sin(q10)*(sin(q9)*(cos(q8)*sin(q5) + sin(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) + cos(q9)*(cos(q5)*cos(q6)*sin(q7) + cos(q5)*cos(q7)*sin(q6)))) + L15*(sin(q9)*(cos(q8)*sin(q5) + sin(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) + cos(q9)*(cos(q5)*cos(q6)*sin(q7) + cos(q5)*cos(q7)*sin(q6))) - L11*cos(q5)*sin(q6) + d1*cos(q5)*cos(q6) - L13*sin(q5)*sin(q8) + L14*cos(q9)*(cos(q8)*sin(q5) + sin(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7))) + L13*cos(q8)*(cos(q5)*cos(q6)*cos(q7) - cos(q5)*sin(q6)*sin(q7)) - L14*sin(q9)*(cos(q5)*cos(q6)*sin(q7) + cos(q5)*cos(q7)*sin(q6)) + L12*cos(q5)*cos(q6)*cos(q7) - L12*cos(q5)*sin(q6)*sin(q7);

Y := L10*sin(q5) - L9 + L16*(sin(q10)*(cos(q5)*sin(q8) - cos(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) - cos(q10)*(sin(q9)*(cos(q5)*cos(q8) + sin(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) - cos(q9)*(cos(q6)*sin(q5)*sin(q7) + cos(q7)*sin(q5)*sin(q6)))) + d2*(cos(q10)*(cos(q5)*sin(q8) - cos(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) + sin(q10)*(sin(q9)*(cos(q5)*cos(q8) + sin(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) - cos(q9)*(cos(q6)*sin(q5)*sin(q7) + cos(q7)*sin(q5)*sin(q6)))) - L15*(sin(q9)*(cos(q5)*cos(q8) + sin(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) - cos(q9)*(cos(q6)*sin(q5)*sin(q7) + cos(q7)*sin(q5)*sin(q6))) + L13*cos(q5)*sin(q8) - L11*sin(q5)*sin(q6) + d1*cos(q6)*sin(q5) - L14*cos(q9)*(cos(q5)*cos(q8) + sin(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5))) - L13*cos(q8)*(sin(q5)*sin(q6)*sin(q7) - cos(q6)*cos(q7)*sin(q5)) - L14*sin(q9)*(cos(q6)*sin(q5)*sin(q7) + cos(q7)*sin(q5)*sin(q6)) + L12*cos(q6)*cos(q7)*sin(q5) - L12*sin(q5)*sin(q6)*sin(q7);

Z := L15*(cos(q9)*(cos(q6)*cos(q7) - sin(q6)*sin(q7)) - sin(q8)*sin(q9)*(cos(q6)*sin(q7) + cos(q7)*sin(q6))) - L11*cos(q6) - L8 - d1*sin(q6) + L16*(cos(q10)*(cos(q9)*(cos(q6)*cos(q7) - sin(q6)*sin(q7)) - sin(q8)*sin(q9)*(cos(q6)*sin(q7) + cos(q7)*sin(q6))) - cos(q8)*sin(q10)*(cos(q6)*sin(q7) + cos(q7)*sin(q6))) - d2*(sin(q10)*(cos(q9)*(cos(q6)*cos(q7) - sin(q6)*sin(q7)) - sin(q8)*sin(q9)*(cos(q6)*sin(q7) + cos(q7)*sin(q6))) + cos(q8)*cos(q10)*(cos(q6)*sin(q7) + cos(q7)*sin(q6))) - L13*cos(q8)*(cos(q6)*sin(q7) + cos(q7)*sin(q6)) - L14*sin(q9)*(cos(q6)*cos(q7) - sin(q6)*sin(q7)) - L12*cos(q6)*sin(q7) - L12*cos(q7)*sin(q6) - L14*cos(q9)*sin(q8)*(cos(q6)*sin(q7) + cos(q7)*sin(q6));

 

I need to optimize these equations, but still keep them separate. I would like to use mutual expressions for the calculations within, but still as I said keep the outputs of X, Y and Z separate.

This is MATLAB code.

 

Thanks in advance for any help.

Hi,

 

I am new to Maple and have a problem when solving three equations with three variables. But when  I plug in into solve function then it gives no answer.

eqn1 := 24900 = A*exp(-X*1.293995859*10^22)+A*exp(-Y*1.293995859*10^22)+5852.27;

eqn2 := 6000 = A*exp(-X*1.293995859*10^22)+2422.929937;

eqn3 := 19100 = A*exp(-Y*1.293995859*10^22)+8275.199937;

Variables are [A,X,Y]


plot(x^2, x = -2 .. 2)

Error, (in plot) incorrect first argument x^2

 

plot(2);

 

solve(x-1 = 0, x)

Error, (in coulditbe) invalid input: `coulditbe/internal` uses a 1st argument, obj, which is missing

 

``


Download Maple_Worksheet.mw

Hi,

I'm using Maple 18 and none of my worksheets that I've developed on earlier versions work on it. I tried starting a new worksheet with a very simple command (attached) and even that's giving me problems. As you can see, I have no trouble plotting constant functions, but as soon as I put in a variable it breaks down. It won't solve equations either.

FYI I'm using an HP G72 laptop with Windows 7 and no installation issues came up.

Can anyone tell me what's going on here?

Thanks,

Tom

In this section, we will consider several linear dynamical systems in which each mathematical model is a differential equation of second order with constant coefficients with initial conditions specifi ed in a time that we take as t = t0.

All in maple.

 

Vibraciones.mw

(in spanish)

 

Atte.

L.AraujoC.

Hi there

I'm trying to isolate (y1-3)2+(x1-1)in the equation 25(y1-3)2+200+100(x1-1)2=0.

I have tried isolate and solve, but solve coplains about solving for expressions (but when inputting i:=(x1,y1)->(y1-3)2+(x1-1)2 it still doesn't work), and isolate can only isolate either (y1-3)2 or (x1-1). Not both.

How can I do this with as few lines as possible?

Thanks

- Alex

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