Dear Maple users

Physical experiment: I dropped a ball with low mass from a height of approximately 7 meters and wanted to test if the air resistance was proportional to the square of the velocity. I filmed the fall and used the program Logger Pro to collect data: a number of datapoints (time,height) was collected. I copy/pasted the datapoints into MS Excel, from where I could import data into Maple via Tools > Assistants > Import Data ... Then I wanted to make a fit with the theoretical solution, given by a function having just one parameter: the Drag coefficient. Unfortunately I received an error "complex values encountered" (see below). I can solve the problem manual by making a number of guesses for the drag coefficient, until the theoretical curve approximates the data points well. I wanted to make Maple do the fitting job, though. I will appreciate if someone could give an idea how to fit the data properly.

NB! Mass m and g is defined above in the Maple document. The Statistics and plots package is called too.

Suppose we have a differential equation that it's order is 2. For example

diff(x(t), t, t)+(1000*(x(t)^2-1))*(diff(x(t), t))+x(t) = 0,

and we want to solve it numerically. When we use some initial values and dsolve it, the maple solves it very quickly. We can plot each new equations of x(t) without any problem respect of "t" or else.

But when we want to show the variation of "diff(x(t), t, t)" respect of "t" (when our derivation order is equal or upper than our differential equation order) our answer is 0 however dx(t)/dt is not 0 or constant!

What's happen here?

I tested it with all kind of methods as "rkf45","rosenbrock","lsode" etc.  but non of them showed me a correct answer.

How can I solve it correctly?
 
  
Please help me!

Hi all

How I use "solve" or "fsolve" for this equation ?

M2 := evalf[4](Matrix(4, 4, {(1, 1) = BesselJ(0, 0.5e-1*sqrt(0.1111111111e-16*omega^2-25.00027778)), (1, 2) = -BesselJ(0, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25)), (1, 3) = -BesselY(0, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25)), (1, 4) = 0, (2, 1) = (0.1111111111e-16*I)*omega*(1-25000000000000/omega^2)*BesselJ(1, 0.5e-1*sqrt(0.1111111111e-16*omega^2-25.00027778))/sqrt(0.1111111111e-16*omega^2-25.00027778), (2, 2) = -(0.4444444444e-16*I)*BesselJ(1, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (2, 3) = (0.4444444444e-16*I)*BesselY(1, 0.5e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (2, 4) = 0, (3, 1) = 0, (3, 2) = BesselJ(0, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25)), (3, 3) = BesselY(0, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25)), (3, 4) = -BesselY(0, 0.60e-1*sqrt(0.1111111111e-16*omega^2-25)), (4, 1) = 0, (4, 2) = (0.4444444444e-16*I)*BesselJ(1, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (4, 3) = (0.4444444444e-16*I)*BesselY(1, 0.60e-1*sqrt(0.4444444445e-16*omega^2-25))/sqrt(0.4444444445e-16*omega^2-25), (4, 4) = -(0.1111111111e-16*I)*omega*BesselY(1, 0.60e-1*sqrt(0.1111111111e-16*omega^2-25))/sqrt(0.1111111111e-16*omega^2-25)})):

with(LinearAlgebra):
DETM2 := Determinant(M2):
solve(DETM2 = 0, omega);

Error, (in solve) cannot solve for an unknown function with other operations in its arguments

Is this Error because of combination of bessel functions? if I use asymptatic forms, does it work?

Thanks

Dear all;

Thanks in advance for helping me to plot the solution of this second order ode.

with(plots):
ode := diff(y(x), x, x) = x*y(x)+x^(17/12);
ics := y(1000) = 0, y(1001) = 1;
 dsolve({ics,ode}):

How can I plot the solution obtained in the range (1000, 1001).

Thanks

How to produce such a plot with Maple?


The difficulty is that the geom3d package does not include a command for a cylinder whereas
the plottools package has the cylinder command, but does not have a tool to determine whether
two random cylinders intersect.

I would like to plot the following singular double integral, but I cannot due to singularities...

where x>0, t=0.2 and m=0.2.

I defined f(y) function as f:=y->exp(-(y-4.68)^2/0.4):

I attached my file:
1st_try.mw

Thank you !

There is an error in my implementation as follow:

"Error, (in unknown) incorrect syntax in parse: `*` unexpected (near 1st character of parsed string)"

What I have to do to remove this error?

This is the code hw2_final.mw

This is the warning 

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters )"

How to solve it?

Hello everyone,

I am trying to extract the coefficients from a differential poynomial. In general, this poynomial is in two variables, say u and v along with their differentials, i.e D(u) or D@@2(u) or so on. 

Coefficients of this polynomials are rational funcitons.

For instance- consider the following example:

a(x)*v*u+v*D(u)-D(v)*u

then output should be [a(x), 1, -1].

Thanks for your help.

Hello,

I've got this error in my code and I don't know why as I didn't get it when I used a different xn function. Any help would be greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man

Download First_part_fractal_determination_.mw

Explore the values of km digit(n,m) using km list for all m, 0 ≤ m ≤ 8.
Look at the output until you can make a conjecture that concerns the pattern
obtained for each fixed m, 0 ≤ m ≤ 8 using 

km := proc (n::posint, m::nonnegint)

local k,

mySum := 0;

for k to n do

mySum := mySum+k^m

end do;

return mySum

end proc

using a list km list(m,6,20) when m is not a multiple of 4, and km list(m,6,50) when m is a multiple of 4.

any help appreciated..THank you

i have this problem -> f'^2 -ff''=f'''-k1(2f'f'''-ff''''-f''^2)+Ha^2(E1-f') with boundary conditions f(0)=0, f'(0)=1, f'(∞)=0.

since it is a fourth order equation, but only three bcs, it does not produce unique solution. so the solution of the equation may be seek in form of f=f0(eta)+k1f1(eta).

thus the equation will become 

f0'^2-f0f0''=f0'''+Ha^2(E1-f0')

and

f1'''-Ha^2f1'-2f0'f1'+f0f1''+f1f0''=2f0'f0'''-f0f0''''-f0''^2.

boundary conditions are 

f0(0)=0,f0'(0)=1,f0'(∞)=0

f1(0)=0,f1'(0)=0,f1'(∞)=0.

i had been clueless in solving this problem. please somebody help me with this problem.

Dear all,

I have the function

y:=x->-9.8455282400*10^9142*exp(-(2/3)*x^(3/2))/(x^(1/4)*sqrt(Pi))+3.3889331940*10^(-9169)*exp((2/3)*x^(3/2))/(x^(1/4)*sqrt(Pi))+(16/153)*x^(7/6)*sqrt(Pi)*exp((2/3)*x^(3/2))+Pi*((1/2)*exp(-(2/3)*x^(3/2))*(-1+exp((2/3)*x^(2/3)))/(x^(1/4)*Pi)-(16/153)*x^(7/6)*exp((2/3)*x^(3/2))/sqrt(Pi));

how can I plot y versus x with x in the interval (1000, 1001).

First, it's simple to verify that y(1000)=0; y(1001)=1;  So (1000, 0) and (1001,1)  belong to our graph.

I tried plot( y, x=1000..1001); but there is no curves.

Thank you in advance to help me to plot the graph of this function.

with brest regards,

defining f:=(t,a,b,c)->a*b/c*t^2 how can I give values for a,b and c inside the plot command?

plot(f(t,a,b,c),t=0..10 ????)

Staffan

Hi Please I need help with making the output of my fslolve appear in a way that I can easily copy to an excel.

I am doing analysis for 3 countries and each time I produce a result I copy manually to excel and use 'text to column' and the 'transpose' excel options to arrange the results in order. I do this for almost 20 time because I want to see how hows in parameter affect the variables. is there a way I can convert this to a 32 by 3 matrix so that I can copy all at the same time instead of copying each variable at a time. here is my solve command

UK_SOL_FIRST:= fsolve(eval({eq||(1..32)}, Params_UK_FIRST), InitValue_UK_FIRST);
ES_SOL_FIRST:= fsolve(eval({eq||(1..32)}, Params_ES_FIRST), InitValue_ES_FIRST);
DK_SOL_FIRST:= fsolve(eval({eq||(1..32)}, Params_DK_FIRST), InitValue_DK_FIRST);

The Results

UK_SOL_FIRST:={A_ss = 14.36104896, C_ss = 1.445842138, I_ss = 0.3136706500,

K_ss = 12.54682600, K_v_ss = 125.4682600,

LT_ss = 0.01061009037, L_ss = 4.014721807, N_ss = 0.9307582996,

P_a_ss = 0.9336893751, P_ss = 0.8625403648,

Surp = 0.9890479879, U_b_ss = 0.1781599919,

U_ss = 0.1046105158, V_ss = 0.05052687912, W_max = 1.476989982,

W_min = 0.4879419937, W_ss = 1.826907218,

W_tilde = 3.478049987, Y_ss = 2.428417935, aa_ss = 21.67403493,

chhi = 0.4523413798, f_c_ss = 0.04880034560,

m_ss = 0.03536881539, p_d_ss = 0.9907986980,

x_T = 0.7023268636, y_d_ss = 10.57030302, y_f_ss = 1.174478111,

y_x_ss = 10.57030300, z_ss = 21.14060602,

Profit_ss = 4.094720376, phi_prod = 0.9753885739,

theta_ss = 0.4830000000}

ES_SOL_FIRST:={A_ss = 10.91702785, C_ss = 2.038687975, I_ss = 0.3058575000,

K_ss = 12.23430000, LT_ss = 0.1309315222, L_ss = 2.857497927,

N_ss = 0.8398656215, P_a_ss = 0.9680877046,

P_ss = 0.8638978804, Surp = 2.541617932, U_b_ss = 0.9095925505,

U_ss = 0.1819708847, V_ss = 0.03119500880, W_max = 3.252738093,

W_min = 0.7111201606, W_ss = 3.605202340,

W_tilde = 3.665280790, Y_ss = 2.367929032, aa_ss = 15.67939783,

betta = 0.9909865708, chhi = 0.2898275349,

f_c_ss = 0.6743530978, m_ss = 0.02183650616,

p_d_ss = 0.9939322922, x_T = 0.005556307841,

y_d_ss = 7.853422751, y_f_ss = 1.195945300,

y_x_ss = 7.978400682, z_ss = 15.83182343,

Profit_ss = 3.084421270, phi_prod = 1.009721394,

theta_ss = 0.1714285714}

DK_SOL_FIRST:={A_ss = 16.18893837, C_ss = 1.359886068, I_ss = 0.2487000000,

K_ss = 9.948000000, LT_ss = 0.02282780783, L_ss = 5.834365727,

N_ss = 0.9399351536, P_a_ss = 0.7054445707,

P_ss = 0.8796237740, Surp = 0.6511024854,

U_b_ss = 0.4572819488, U_ss = 0.08450316042,

V_ss = 0.03491187713, W_max = 1.293898615,

W_min = 0.6427961298, W_ss = 2.363825013,

W_tilde = 2.758200925, Y_ss = 1.755529412, aa_ss = 34.56310241,

betta = 0.9851712031, chhi = 0.4499333284,

f_c_ss = 0.1898151486, m_ss = 0.02443831399,

p_d_ss = 1.032636460, x_T = 0.1506134910, y_d_ss = 11.17773688,

y_f_ss = 0.9144278497, y_x_ss = 13.74561008,

z_ss = 24.92334696, Profit_ss = 4.926248216,

phi_prod = 0.7210969276, theta_ss = 0.4131428571}