How to draw the following function containing an imaginary number
 

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I'm attempting to solve the complex-valued differential equation

restart:
assume(t::real):

pde := diff(A(t),t) - I * conjugate(A(t))*A(t)^2 = 0:
dsolve(pde);

However, it seems Maple attempts to solve it using separation of variables and gives

t-Intat(-I/conjugate(_a)/_a^2,_a = A(t))+_C1 = 0

Unless I'm mistaken, a complex integral such as this isn't even defined without a contour.

Working the integral out by hand, I know the solution to be

_C1*exp(I*abs(_C1)*t)

Is there a trick I'm missing to get Maple to find this solution? Or is this outside the scope of what Maple can handle on it's own?

Thanks!

I believe I am having memory issues which is causing the MAPLE kernal to terminate.  If I assign m a value then it seems to work, but I would like to leave m unassigned so that S1 can later be evaluated for any arbitrary m.  Is there a way around this?

Download MAPLE_crashing.mw

Hello everybody

I am currently having trouble 'manually simplifying' an equation that I differentiated using maple. Basically, the equation that I get involves hessian-matrices. Since the resulting equation is rather long, I would like to replace every such matrix by a sign, say H.
This is easy to do for non-matrix equations, i.e.

subs(sin(x)sin(y) = z, sin(x)sin(y) + xy)

will give me , which looks a bit easier.

However, I couldn't figure out how to do a similar thing with matrices. For example, the following code

subs(Matrix(3, 3, [[x, y, z], [y, z, x], [z, x, y]]) = A, Matrix(3, 3, [[x, y, z], [y, z, x], [z, x, y]])+B)

 will not work.
I already thought about converting the matrices first into lists (because for some reason it works for lists). However, I would also like to do the same as above for for functions of matrices, i.e. set , where is a matrix (this also fails, probably for the same reason).

Also, the same thing seems to fail for vectors and general arrays, so I guess the actual problem might be the array type.

I also tried alternative ways, such as or , but the later even gives an error since it cannot handle matrices at all.

This feels a bit like a noob question, but I spent almost 2 days now searching for an answer or a workaround, so my apologies if I missed something trivial.

All the best
Adrian

Hi, I try to solve the below integral. when I press enter key maple dosen't show answer and show the integral again.

int(r*r[bc]*r[tc], r = r[bc] .. r[tc]);

but when I write intgral this way and use " i " as subscript ,maple solve it.

int(r[i]*r[bc]*r[tc], r[i] = r[bc] .. r[tc]);

I just want to know why?

what is difference between first and second integral?

and also is there any way (or any packages) to solve these integrals?

(I read https://www.maplesoft.com/applications/view.aspx?SID=6846&view=html article befor)

thanks.

Good day everyone,

I'm relatively new to Maple, and I study engineering (not maths), so maybe my problem is related to a bad approach of the equations.

The problem is that I'm asking Maple to do a double integral of a "complex" expression and it only solve the first integral, but not the second.

Here is the code:

https://www.dropbox.com/home/C%C3%81LCULO%20FUERZAS

Thanks.

Dears!

Hope everyone should be fine. I am face to import excel sheet in maple. I saved execl sheet with name "Employees.xlsx" at desktop. When I use the following command
S := Import("Employees.xlsx", 1, "A1:B101");

I got the following error. 

"Error, (in ExcelTools:-Import) Could not open the file"

Please help me to fix this problem. I am waiting positive response. 

Special request to:

@Carl Love
@Preben Alsholm
@acer

1. (2*k^3-6*k^2+7*k+15-k*sqrt(k^6-12*k^5+64*k^4-198*k^3+448*k^2-636*k+369))/(-k^4+2*k^3-2*k^2+10*k+15)
2. (k^3+5*k+(-k^2+k)*sqrt(k^4-10*k^3+37*k^2-60*k+180)+30)/(-k^4+k^3+k^2+5*k+30)

Please I am trying to get a compact result for this code in particular the lines assigne "a" and "b" respectively. I am sure the result shoud not be more than two lines. Can someone be of help? 

restart:
P:=a[0]+(a[1]*x)/(1+(a[2]*x)/(1+(a[3]*x))):
Q:=diff(P,x):
T:=diff(P,x,x):
e1:=simplify(eval(P, x=q))=y[n]:
e2:=simplify(eval(Q,x=q))=f[n]:
e3:=simplify(eval(Q,x=q+h))=f[n+1]:
e4:=simplify(eval(T,x=q+h))=g[n+1]:
var:=seq(a[i], i=0..3):
M:=e||(1..4):
Cc:=eval(<var>, solve(eval({M}),{var}) ):
for i from 1 to 4 do
	a[i-1]:=Cc[i]:
end do:
Cf:=P:
a:=y[n+1]=collect(simplify(eval(Cf, x=q+h)),[y[n], f[n], f[n+1],g[n+1]], recursive):
b:=map(eval@allvalues, [a]);

I'm receiving a very interesting error when attempting to solve a system of differntial equations:

{sqrt(2)*sqrt(F1(t))*diff(F2(t),t) = 0}:
% union {F3(t) = 0}:
pdsolve(%, {F1(t),F2(t),F3(t)});

When attempting to run this code, I get the following error:

Error, (in pdsolve/sys) invalid input: DifferentialAlgebra:-DifferentialRing expects value for keyword parameter blocks to be of type {undefined, Or(list({name, unknown, list({name,unknown})}),name,unknown)}, but received [F3, F2, _F1 = (NULL), F1 = [_F1, F1], _F2] 

Interestingly, removing the second line, or even the sqrt(2), allows the calculation to proceed correctly. It this a bug, or am I doing something wrong?

Thank you very much!

(I'm aware this would technically be a system of ODEs, not PDEs; my actual code includes additional partial derivatives. Additionally, dsolve appears to only generate a trivial solution in this case).

Hey folks.

I need to do a kind of loop calc. in maple and im not shure how to. 

lets say i guess a temperature T.

i then put it through all soughts of eqations where the variabel T is necessary for the outcome of my result, which i then use again as T. the loop should finish when T as a result is the same as my guess in the beginning. like:

T:=45 

bla bla calculation

T_new:= 35

again 

T:=35

bla bla calculation

T_new= 35 

Finish!!

Any ideas?

Dear sir I want to plot the graph for different values of F=0.1, F=0.2,F=0.5 . My codes are given and i am attaching the sample graph. For F=0.1, Nb=0.1,0.2,0.3 three curves

Similarly For F=0.2,Nb=0.1,0.2,0.3 three curves and for F=0.5, Nb=0.1,0.2,0.3 three curves. Total nine curves 

restart:
h:=z->1-(delta2/2)*(1 + cos(2*(Pi/L1)*(z - d1 - L1))):
K1:=((4/h(z)^4)-(sin(alpha)/F)-h(z)^2+Nb*h(z)^4):
lambda:=Int(K1,z=0..1):

L1:=0.2:
d1:=0.2:
alpha:=Pi/6:
plot( [seq(eval(lambda, Nb=j), j in [0.1,0.2,0.3])], delta2=0.02..0.1);

please how can I simplify the results of assigned K cum each of the coefficients further in the following code? the results are too large.

restart:
#k=2:
omega:=u/h:
psi:=v/h:
t:=(sum(a[j]*x^j,j=0..2)+a[3]*sin(omega*x)+a[4]*cos(omega*x)+a[5]*sin(psi*x)+a[6]*cos(psi*x)):
F:=diff(t,x):
G:=diff(t,x,x):
p1:=simplify(eval(t,x=q+h))=y[n+1]:
p2:=simplify(eval(F,x=q))=f[n]:
p3:=simplify(eval(F,x=q+h))=f[n+1]:
p4:=simplify(eval(F,x=q+2*h))=f[n+2]:
p5:=simplify(eval(G,x=q))=g[n]:
p6:=simplify(eval(G,x=q+h))=g[n+1]:
p7:=simplify(eval(G,x=q+2*h))=g[n+2]:
vars:= seq(a[i],i=0..6):
Cc:=eval(<vars>, solve({p||(1..7)}, {vars})):
for i from 1 to 7 do
	a[i-1]:=Cc[i]:
end do:
Cf:=t:

K:= collect(combine(simplify(eval(Cf,x=q+2*h),size),trig),{y[n+1],f[n],f[n+1],f[n+2],g[n],g[n+1],g[n+2]},factor):


alpha[1]=simplify(coeff(K,y[n+1]));
beta[0]=simplify(coeff(K,f[n]),size);
beta[1]=simplify(coeff(K,f[n+1]),size):
beta[2]=simplify(coeff(K,f[n+2]),size):
gamma[0]=simplify(coeff(K,g[n]),size):
gamma[1]=simplify(coeff(K,g[n+1]),size):
gamma[2]=simplify(coeff(K,g[n+2]),size):

I need to plot a trajectory where the horizontal equation is x(t) = 4t and the vertical is y(t)=4t-0.5t^2

How would I plot the two equations at once to make a trajectory?

If someone could please explain how to do it (also doing it would be nice) because I'm sure I'll have to do it again.

How do I apply select to a set element-wise?

I have defined a procedure which computes the order of an element g mod p.

findOrderOf:=proc(g,p)
  local i:=1;
  local gpwr:=1;
  for i from 1 to p-1 do
    gpwr:=gpwr*g mod p;
    if(gpwr = 1) then:
      return i;
    end if:
  end do:
end proc:

I then want to select the primes which are generated by 2 and 3.

primes:=select(isprime,[`$`(2000 .. 3000)]);
select(findOrderOf(2,x=p)=p-1 and findOrderOf(3,x=p)=p-1,primes);

I am stuck with how to make the last line work.