## Help with Maple Commands...

Hi I was wondering if you can help me with some maple commands about using Euler's method. My professor created a tutorial on using some commands to calculate the value via Euler's method.

Her commands in the tutorial for using Euler's method  for a differential equation- dy/dx= x+y   y(0)=1

x0:=0:y0:=1:xf:=1:n:=10:

h:=evalf((xf-x0)/n);

f:=(x,y) -> x+y

x:=x0:y:=y0:

This next step confuses me the most, my professor uses this syntax to compute the values of approximation via Euler's method. N represents the number of pieces we want to approximate the value with. X0 is initial and XF is final.

forifrom1tondo k:=f(x,y):y:=y+h*k:x:=x+h:print(x,y):od:

I tried replicating this syntax on the exact same problem, copying the syntax commands word for word. Yet, I keep getting the same error "unable to parce" error, with the "od" being highlighted. But on her tutorial, it gave her an two columns with the intervals (n) and all it's values. She even did the same did for only wanting 1 loop printed

forifrom1tondo k:=f(x,y):y:=y+h*k:x:=x+h:od:print(x,y):.   And it gave her only 1 loop.

## Maple programing problem in for loops...

helo my friends,

## computing the wronskian with Maple gave nothing...

I am tying to compute the wronskian of a fourth order DE: y=C1e2x+ C2e-x +C3xe-x+ C4x2e-x Here's what I did:

with(VectorCalculus):
with(LinearAlgebra):

Determinant(Wronskian([e^(2*x), e^(-x), xe^(-x), x^2*e^(-x)], x)):

which gave nothing.

AJ

## How to extract Real and Imaginary using assumption...

I can't get the Real and Imaginary parts of matrix to seperate out as required. It is an SU(2) matrix. Want to convert is to a 4 Vector (quaternion). I think because Maple doesnt know what psi(t) is being conservative so to speak. Tried assume, assuming...

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## What is my mistake in this simple code?...

Where I made a mistake I got this error in for loop and how to fix it?

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## Problem with functions...

i got this code, but for any n = 2N (par) i get some high errors, my M goes nuts.  anyone knwos wheres my mistake?

With(CurveFitting); Digits; 5; f := proc (x) options operator, arrow; abs(x) end proc; n := 8; h := 2/n; for i from 0 to n do x[i] := h*i-1 end do; for i from 0 to n-1 do L[i] := (product((x-x[j])/(x[i]-x[j]), j = 0 .. i-1))*(product((x-x[k])/(x[i]-x[k]), k = i+1 .. n-1)) end do; lagr := sum(f(x[p])*L[p], p = 0 .. n-1); P := expand(lagr); plot({P, f(x)}, x = -1 .. 1, y = 0 .. 2); M := maximize(abs(abs(x)-P), x = -1 .. 1); M1 := numapprox:-infnorm(abs(abs(x)-P),

x = -1 .. 1)

## My system of equation was ODE, but Maple insists i...

I was trying to solve a system of ODE using Maple, but to my surprise, Maple recognizes diff((phi(t), t)) as a variable which is different than t.

My code is as following:

dsys := {2*m1*(a+l*sin(phi(t)))^2*(diff(diff(theta(t), t), t))+4*m1*(a+l*sin(phi(t)))*l*cos(phi(t))*(diff(theta(t), t))*(diff(phi(t), t)) = M, 2*m1*l^2*(diff(diff(phi(t), t), t))+4*m2*l^2*sin(2*phi(t))*(diff(phi(t), t))*(diff(phi(t), t))+4*m2*l^2*sin(phi(t))^2*(diff(diff(phi(t), t), t))-2*m1*(a+l*sin(phi(t)))*l*cos(phi(t))*(diff(theta(t), t))*(diff(theta(t), t))-2*m2*l^2*(sin(2*phi(t)))(diff(phi(t), t))*(diff(phi(t), t)) = -(2*(m1+m2))*g*l*sin(phi(t))-2*k*l^2*sin(2*phi(t)), phi(0) = 0, theta(0) = 0, (D(phi))(0) = 0, (D(theta))(0) = 0}

subs({M = 10, a = .5, g = 9.81, k = .1, l = .5, m1 = 10, m2 = 1}, dsys);

dsn1 := dsolve(dsys, numeric)

The error I got was Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {t, diff(phi(t), t)}

I don't get why this is happening. Could you show me what's going on?

## How do I generate the recursion...

Please Sir/Ma, I'm trying to generate a recurrent relations of this series and I try to use "if" "else" condition but I didn't get it right. Any one with useful suggestions. Appreciate

restart;
Y[0] := A; Y[1] := B;
if k = a then delta(k-a) := 1 else 0 end if;
0
for k from 0 to 10 do Y[k+2] := solve(add(delta(i-1)*(k-i+1)*(k-i+2)*Y[k-i+2], i = 0 .. k)+add((delta(i)-delta(i-1))*(k-i+1)*Y[k-i+1], i = 0 .. k)+lambda*Y[k] = 0, Y[k+2]) end do;
y := sum(Y[j]*x^j, j = 0 .. 10);

## an error occurred, diff received 0...

Hello, I have a function defined as

g :=  (x, y)->diff(u1(x, y), x, x)+diff(u2(x, y), x, y).

I want to define another function as follows

f :=  (y) ->subs(x = 0, g(x, y)) ,

Now, when I want to calculate numerical values for the new function f(0), f(0.1), f(0.2),..... and so on. The following massage appear

Error, (in f) invalid input: diff received 0, which is not valid for its 2nd argument.

What is the problem here.

Amr

## Trouble taking partial derivatives with e^(y) type...

HI, I'm new to maple and am having trouble taking partial derivitives. I couldn't find anything in the documentation that seemed to resolve the situation, and can't be the first person to stumble through this part of Maple.

Namely, it seems like the exponential function causes an extra "ln()" term to show up in the solution. I've tried with e^(y) and exp^(y) but nothing seems to be working. When i use the same markup up in wolfram and matlab and Ti-CAS i get the "correct" solution.

I attached a screen showing my input and output.

thanks for any insight!

## datatype=float[8] Problem ...

Hello,

I'm trying to solve a system of 9 ODE in a model of a chemical reactor. But, unfortunately, when I try to plot the curves, I get the following error message: Error, (in f) unable to store '[Float(undefined)]+8.5809018712796' when datatype=float[8]

Can anyone help me please? I read some related problems here, but couldnt find a solution yet.

Best regards

## Not solving when specifying value of n?...

This is what I'm trying to solve:

I literally just want it to plug in those values for n and spit out a value. This is easy enough for me to do by hand, but I obviously wanted to speed up the process by doing it with Maple. What's wrong here? I clicked the pink links and that didn't help.

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## error message'' which is not valid for its 1st arg...

hi

how i can remove this error?

1) ''Error, invalid input: lhs received diff(diff(diff(diff(w(x, y, t), x), x), x), x)+.12*(diff(diff(diff(diff(w(x, y, t), x), x), y), y))+0.11e-2*(diff(diff(diff(diff(w(x, y, t), y), y), y), y))+10-.4*(diff(diff(w(x, y, t), x), x))-0.4e-2*(diff(diff(w(x, y, t), y), y))+diff(diff(w(x, y, t), t), t)-w(x, y, t)-tau, which is not valid for its 1st argument, expr'''''

2)'' Error, incorrect number of extra arguments in select''

thanks

 > restart:Digits := 15: beta := 1: alpha := 0.1: Upsilon := .1: xi := 10: eta := .1: N_X := .4: N_Y := .4: psi:=4.73:
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 > BC1:=subs(a=1,b=1,[BC])
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We use the method of multiple scales to directly attack EOM1 and BC1. To transform the time derivatives in EOM1 in terms of the scales  and , we let

 > timeScales:=T[0],T[1]
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 > msForm:={w(x,y,t)=w(x,y,timeScales),seq(diff(w(x,y,t),t\$i)=dt[i](w(x,y,timeScales)),i=1..2)}
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 > multiScales:=`union`(map(s->subs(w=s,msForm),[w])[])
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Then, we seek a second-order approximate solution in the form

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We introduce the detuning  to describe the nearness of the edge lengths  and , consider the case of primary resonance, and hence let

 > tau=epsilon^3*tau(x,y)*convert(cos(Omega*T[0]),exp)
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Substituting multiScales, solRule, and scaleRule2 into EOM1, expanding the result for small , and discarding terms of order higher than , we obtain

 > expr83a:=seq(convert(series(value(subs(multiScales,solRule,lhs(EOM))),epsilon,4),polynom),i=1)

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