Maple 2015 Questions and Posts

These are Posts and Questions associated with the product, Maple 2015

MAPLE 15 on Windows 10

I have a file on which I can no longer open. This happened after my computer made me long on again after being gone for a little while. Maple was not running when I got back on. This is not unusal and I just clinck on the file and restart.

This time this did not work.

It comes up with a message asking me to select an input mode. Whatever I select even 'Plain text' it just hangs.

I'd send you an image, but I don't see how to do it. The button provide only allows for something with  url and the snip I made is on my desktop.

I need to get thiis worksheet back. I've put a lot of effort into it.

-Traruh

hi 

how i can apply this differential in maple?

thabks...

 

hi .please help me for solve this equations.

bbb2.mw

restart; d[11] := 1; mu[11] := 1; q[311] := 1; d[33] := 1; mu[33] := 1; a[11] := 1; e[311] := 1; a[33] := 1; A := 1; g[111111] := 1; c[1111] := 1; g[113113] := 1; f[3113] := 1; beta[11] := 1; `ΔT` := 1; II := 1; L := 1

J := d[11]*(diff(Phi(x, z), x, x))+mu[11]*(diff(psi(x, z), x, x))+q[311]*(diff(w(x), x, x))+d[33]*(diff(Phi(x, z), z, z))+mu[33]*(diff(psi(x, z), z, z));

diff(diff(Phi(x, z), x), x)+diff(diff(psi(x, z), x), x)+diff(diff(w(x), x), x)+diff(diff(Phi(x, z), z), z)+diff(diff(psi(x, z), z), z)

(1)

B := a[11]*(diff(Phi(x, z), x, x))+d[11]*(diff(psi(x, z), x, x))+e[311]*(diff(w(x), x, x))+a[33]*(diff(Phi(x, z), z, z))+d[33]*(diff(psi(x, z), z, z));

diff(diff(Phi(x, z), x), x)+diff(diff(psi(x, z), x), x)+diff(diff(w(x), x), x)+diff(diff(Phi(x, z), z), z)+diff(diff(psi(x, z), z), z)

(2)

R := A*(g[111111]*(diff(u[0](x), x, x, x, x))-c[1111]*(diff(u[0](x), x, x)+(1/2)*(diff((diff(w(x), x))^2, x)))+e[311]*(diff(diff(Phi(x, z), z), x))+q[311]*(diff(diff(psi(x, z), z), x)));

diff(diff(diff(diff(u[0](x), x), x), x), x)-(diff(diff(u[0](x), x), x))-(diff(w(x), x))*(diff(diff(w(x), x), x))+diff(diff(Phi(x, z), x), z)+diff(diff(psi(x, z), x), z)

(3)

S := -II*g[111111]*(diff(w(x), x, x, x, x, x, x))-II*c[1111]*(diff(w(x), x, x, x, x))+A*g[113113]*(diff(w(x), x, x, x, x))-A*f[3113]*(diff(diff(Phi(x, z), z), x, x))-A*(c[1111]*(diff(u[0](x), x, x)+(1/2)*(diff((diff(w(x), x))^2, x)))+e[311]*(diff(diff(Phi(x, z), z), x))+q[311]*(diff(diff(psi(x, z), z), x)))*(diff(w(x), x))-A*(diff(w(x), x, x))*(c[1111]*(diff(u[0](x), x)+(1/2)*(diff(w(x), x))^2)+e[311]*(diff(Phi(x, z), z))+q[311]*(diff(psi(x, z), z))-beta[11]*`ΔT`);

-(diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x))-(diff(diff(diff(Phi(x, z), x), x), z))-(diff(diff(u[0](x), x), x)+(diff(w(x), x))*(diff(diff(w(x), x), x))+diff(diff(Phi(x, z), x), z)+diff(diff(psi(x, z), x), z))*(diff(w(x), x))-(diff(diff(w(x), x), x))*(diff(u[0](x), x)+(1/2)*(diff(w(x), x))^2+diff(Phi(x, z), z)+diff(psi(x, z), z)-1)

(4)

dsys := {B, J, R, S}; BCS := {D@@2*w(0) = 0, D@@2*w(L) = 0, Phi(x = 0) = 0, Phi(x = L) = 0, Phi(z = -(1/2)*h) = 0, Phi(z = (1/2)*h) = 0, psi(x = 0) = 0, psi(x = L) = 0, psi(z = -(1/2)*h) = 0, psi(z = (1/2)*h) = 0, w(x = 0) = 0, w(x = L) = 0, u[0](x = 0) = 0, u[0](x = L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, (D(u[0]))(0) = 0, (D(u[0]))(L) = 0}

{D@@2*w(0) = 0, D@@2*w(L) = 0, Phi(x = 0) = 0, Phi(x = L) = 0, Phi(z = -(1/2)*h) = 0, Phi(z = (1/2)*h) = 0, psi(x = 0) = 0, psi(x = L) = 0, psi(z = -(1/2)*h) = 0, psi(z = (1/2)*h) = 0, w(x = 0) = 0, w(x = L) = 0, u[0](x = 0) = 0, u[0](x = L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, (D(u[0]))(0) = 0, (D(u[0]))(L) = 0}

(5)

dsol5 := dsolve(dsys, numeric)

Error, (in dsolve/numeric/process_input) missing differential equations and initial or boundary conditions in the first argument: dsys

 

NULL

NULL

NULL

if former equations are not solvable , please help me for another way, in which at first two equation solve..in this way in equation [J and B] assume that q[311]=e[311]=0 and dsolve perform to find Φ and  ψ

after by finding Φ and  ψ is use for detemine w and u0

please see attached file below[bbb2_2.mw]

bbb2_2.mw

Download bbb2.mw

hi.please help me for solve this equation

i encounter with error''

Error, (in StringTools:-IsPrefix) second argument must be a string''

equations which be solved attached as pdf file

thanks

Kernel4.mw

root.pdf


 

restart

with(LinearAlgebra):

Typesetting:-Settings(functionassign=false):

NULL

Constants

 

landa := 0.404e11; -1; mu := 0.27e11; -1; alpha := 0.23e-4; -1; rho := 2707; -1; k := 204; -1; c := 903; -1; nu := .3; -1; E := 0.70e11; -1; T0 := 293; -1; omega := 0.1e-1

0.1e-1

(1.1.1)

beta := alpha*(3*landa+2*mu):

NULL

varpi := 0.1e-1; -1; No := 15

15

(1.1.2)

 

 

Eq[1] := besselj(0, xi*b)*(eval(diff(bessely(0, xi*r), r), r = a))-(eval(diff(besselj(0, xi*r), r), r = a))*bessely(0, xi*b):

 

wf1 := unapply(Eq[1], xi):

1

 

1.794010904

 

1

 

2

 

1.794010904

 

1

 

3

 

4.802060761

 

2

 

4

 

4.802060761

 

2

 

5

 

4.802060761

 

2

 

6

 

7.908961712

 

3

 

7

 

7.908961712

 

3

 

8

 

7.908961712

 

3

 

9

 

11.03509457

 

4

 

10

 

11.03509457

 

4

 

11

 

11.03509457

 

4

 

12

 

11.03509457

 

4

 

13

 

14.16798650

 

5

 

14

 

14.16798650

 

5

 

15

 

14.16798650

 

5

 

16

 

17.30400975

 

6

(1.2.1)

Eq[2] := MTM:-besselj(1, eta*b)*(eval(diff(MTM:-bessely(1, eta*r), r), r = a))-(eval(diff(MTM:-besselj(1, eta*r), r), r = a))*MTM:-bessely(1, eta*b):

wf2 := unapply(Eq[2], eta):

1

 

1.958510605

 

1

 

2

 

1.958510605

 

1

 

3

 

4.857021628

 

2

 

4

 

4.857021628

 

2

 

5

 

4.857021628

 

2

 

6

 

7.941288451

 

3

 

7

 

7.941288451

 

3

 

8

 

7.941288451

 

3

 

9

 

11.05802155

 

4

 

10

 

11.05802155

 

4

 

11

 

11.05802155

 

4

 

12

 

11.05802155

 

4

 

13

 

14.18576207

 

5

 

14

 

14.18576207

 

5

 

15

 

14.18576207

 

5

 

16

 

17.31852918

 

6

(1.2.2)

 

for m to MM do K0[m] := proc (r, m) options operator, arrow; BesselJ(0, xi[m]*r)*BesselY(0, xi[m]*b)-BesselJ(0, xi[m]*b)*BesselY(0, xi[m]*r) end proc; KK0[m] := proc (r, m) options operator, arrow; diff(K0[m](r, m), r) end proc; K1[n] := proc (r, n) options operator, arrow; BesselJ(1, eta__n*r)*BesselY(1, eta__n*b)-BesselJ(1, eta__n*b)*BesselY(1, eta__n*r) end proc; KK1[n] := proc (r, n) options operator, arrow; diff(K1[n](r, n), r) end proc end do

proc (r, m) options operator, arrow; BesselJ(0, xi[m]*r)*BesselY(0, xi[m]*b)-BesselJ(0, xi[m]*b)*BesselY(0, xi[m]*r) end proc

 

proc (r, m) options operator, arrow; MTM:-diff(K0[m](r, m), r) end proc

 

proc (r, n) options operator, arrow; BesselJ(1, eta__n*r)*BesselY(1, eta__n*b)-BesselJ(1, eta__n*b)*BesselY(1, eta__n*r) end proc

 

proc (r, n) options operator, arrow; MTM:-diff(K1[n](r, n), r) end proc

 

proc (r, m) options operator, arrow; BesselJ(0, xi[m]*r)*BesselY(0, xi[m]*b)-BesselJ(0, xi[m]*b)*BesselY(0, xi[m]*r) end proc

 

proc (r, m) options operator, arrow; MTM:-diff(K0[m](r, m), r) end proc

 

proc (r, n) options operator, arrow; BesselJ(1, eta__n*r)*BesselY(1, eta__n*b)-BesselJ(1, eta__n*b)*BesselY(1, eta__n*r) end proc

 

proc (r, n) options operator, arrow; MTM:-diff(K1[n](r, n), r) end proc

 

proc (r, m) options operator, arrow; BesselJ(0, xi[m]*r)*BesselY(0, xi[m]*b)-BesselJ(0, xi[m]*b)*BesselY(0, xi[m]*r) end proc

 

proc (r, m) options operator, arrow; MTM:-diff(K0[m](r, m), r) end proc

 

proc (r, n) options operator, arrow; BesselJ(1, eta__n*r)*BesselY(1, eta__n*b)-BesselJ(1, eta__n*b)*BesselY(1, eta__n*r) end proc

 

proc (r, n) options operator, arrow; MTM:-diff(K1[n](r, n), r) end proc

 

proc (r, m) options operator, arrow; BesselJ(0, xi[m]*r)*BesselY(0, xi[m]*b)-BesselJ(0, xi[m]*b)*BesselY(0, xi[m]*r) end proc

 

proc (r, m) options operator, arrow; MTM:-diff(K0[m](r, m), r) end proc

 

proc (r, n) options operator, arrow; BesselJ(1, eta__n*r)*BesselY(1, eta__n*b)-BesselJ(1, eta__n*b)*BesselY(1, eta__n*r) end proc

 

proc (r, n) options operator, arrow; MTM:-diff(K1[n](r, n), r) end proc

 

proc (r, m) options operator, arrow; BesselJ(0, xi[m]*r)*BesselY(0, xi[m]*b)-BesselJ(0, xi[m]*b)*BesselY(0, xi[m]*r) end proc

 

proc (r, m) options operator, arrow; MTM:-diff(K0[m](r, m), r) end proc

 

proc (r, n) options operator, arrow; BesselJ(1, eta__n*r)*BesselY(1, eta__n*b)-BesselJ(1, eta__n*b)*BesselY(1, eta__n*r) end proc

 

proc (r, n) options operator, arrow; MTM:-diff(K1[n](r, n), r) end proc

 

proc (r, m) options operator, arrow; BesselJ(0, xi[m]*r)*BesselY(0, xi[m]*b)-BesselJ(0, xi[m]*b)*BesselY(0, xi[m]*r) end proc

 

proc (r, m) options operator, arrow; MTM:-diff(K0[m](r, m), r) end proc

 

proc (r, n) options operator, arrow; BesselJ(1, eta__n*r)*BesselY(1, eta__n*b)-BesselJ(1, eta__n*b)*BesselY(1, eta__n*r) end proc

 

proc (r, n) options operator, arrow; MTM:-diff(K1[n](r, n), r) end proc

(1.2.3)

U1 := -(int(r*K0[m]*(diff(K1[n], r)+K1[n]/r), r = a .. b))/(int(r*K0[m]^2, r = a .. b)); -1; U2 := -(int(r*K1[n]*(diff(K0[m], r)), r = a .. b))/(int(r*K1[n]^2, r = a .. b)); -1; U3 := (int(r^2*omega^2*K1[n], r = a .. b))/(int(r*K1[n]^2, r = a .. b))

0.1555555555e-3/K1[0]

(1.2.4)

m := 0; -1; for m to MM do M__m := int(r*K1[m](r, m)^2, r = a .. b); bb__m := 1/M__m end do

int(r*K1[1](r, 1)^2, r = 1 .. 2)

 

1/(int(r*K1[1](r, 1)^2, r = 1 .. 2))

 

int(r*K1[2](r, 2)^2, r = 1 .. 2)

 

1/(int(r*K1[2](r, 2)^2, r = 1 .. 2))

 

int(r*K1[3](r, 3)^2, r = 1 .. 2)

 

1/(int(r*K1[3](r, 3)^2, r = 1 .. 2))

 

int(r*K1[4](r, 4)^2, r = 1 .. 2)

 

1/(int(r*K1[4](r, 4)^2, r = 1 .. 2))

 

int(r*K1[5](r, 5)^2, r = 1 .. 2)

 

1/(int(r*K1[5](r, 5)^2, r = 1 .. 2))

 

int(r*K1[6](r, 6)^2, r = 1 .. 2)

 

1/(int(r*K1[6](r, 6)^2, r = 1 .. 2))

(1.2.5)

MM; 1; n; 1; m; 1; U1; 1; U2; 1; U3; 1; xi

6

 

0

 

7

 

-(2/3)*K1[0]/K0[7]

 

0

 

0.1555555555e-3/K1[0]

 

xi

(1.2.6)

for m to MM do for n to MM do dsys := {diff(S[m][n](t), t, t, t)+xi^2*[m]*(diff(S[m][n](t), t, t))+(-U1*U2+`η__η__n__`^2)*(diff(S[m][n](t), t))+xi[m]^2*`η__η__n__`^2*S[m][n](t) = -(2*U2*bb[m]/(Pi*xi[m])*(-BesselJ(0, xi[m]*b)/BesselJ(1, xi[m]*a)))*q+xi^2*[m]*U3} end do end do; sol := dsolve(dsys)

Error, (in StringTools:-IsPrefix) second argument must be a string

 

 

NULL

for m to MM do for n to MM do dsys2 := {diff(Q__mn(t), t, t, t)+xi[m]^2*(diff(Q__mn(t), t, t))+(-U1*U2+eta__n^2)*(diff(Q__mn(t), t))+xi[m]^2*eta__n^2*Q__mn(t) = -2*BesselJ(0, xi[m]*b)*U1*U2*b__m*(1-exp(-xi[m]^2*t))/(BesselJ(1, xi[m]*a)*Pi*xi[m]^3)} end do end do;

sol2 := dsolve(dsys2)

Error, (in dsolve) invalid input: `PDEtools/sdsolve` expects its 1st argument, SYS, to be of type Or(set({`<>`, `=`, algebraic}), list({`<>`, `=`, algebraic}), `casesplit/ans`(list, list)), but received [{Q__mn(t)*pochhammer(1-n, n)+(1497143767/5000000)*(diff(Q__mn(t), [`$`(t, t)]))+eta__n^2*(diff(Q__mn(t), t))+(1497143767/5000000)*eta__n^2*Q__mn(t) = 0}]

 

``

NULL

NULL

 

Download Kernel4.mw

When I used exportplot in Maple2015 , the GIF file made easily after Enter. But when I use Engine.evaluate in Java jOpenMaple. it works for every command but exportplot. It didn't create any GIF file. I'm working on project must be use this for create animation by Maple but now that make big trouble. Any one to help this ?

VeHinhNemXien := proc(Alpha,Vbd)
  local Y,V0,alpha,X,ball,Xmax,bgr;
  with(plottools):
  with(plots):
  Y := unapply(V0*sin(alpha)*X/(V0*cos(alpha)) - 1/2*9.8*(X/(V0*cos(alpha)))^2,alpha,V0,X);
  ball := proc(x,y) plots[pointplot]([[x,y]],color=red,symbol=solidcircle,symbolsize=40) end proc;
  Xmax := 2*Vbd^2*sin(Alpha)*cos(Alpha)/9.8;
  bgr := plot(Y(Alpha,Vbd,X),X=0..Xmax,linestyle=[2]);
  animate(ball,[X,Y(Alpha,Vbd,X)],X=0..Xmax,scaling=constrained,labels=["Độ xa","Độ cao"],frames=60,background=bgr);
  exportplot(FileTools:-JoinPath([FileTools:-TemporaryDirectory(), "dothi.gif"]), animate(ball,[X,Y(Alpha,Vbd,X)],X=0..Xmax,scaling=constrained,labels=["Độ xa","Độ cao"],frames=60,background=bgr), gif);
end proc:

save VeHinhNemXien , "D:\\VeHinhNemXien.m";

in java file

String a[];
        a = new String[1];
        a[0] = "java";
        t = new Engine(a, new EngineCallBacksDefault(), null, null);

        t.restart();
        t.evaluate("read \"resources/VeHinhNemXien.m\";");

        t.evaluate(....query to call VeHinhNemXien to draw plot).

I checked carefully. When call it on Maple, it created GIF, but not in java. I checked queryString carefully.

New Info. I find that when I t.evaluate(....query to call VeHinhNemXien to draw plot) . this code make java stop there. that mean no code after this line can run.

 

Hello everyone,

I have an issue that I don't know how to solve.
I would like to plot a part of a surface that is enclosed by another surface. I wrote a proc() function with an if statement and when the statement is statisfienied I returned desired function. The roblem is that if statement gets ploted as well..

Here is my proc()

yield := proc (sigma__x, sigma__y, tau__xy, sigma__cx, sigma__cy, f__45, f__cx, f__cy, tau__u, f__tx, f__ty, alpha)

if eval(evalf(f__r(sigma__x, sigma__y, tau__xy, f__tx, f__ty, alpha)) < 0) then

return f__h(sigma__x, sigma__y, tau__xy, sigma__cx, sigma__cy, f__45, f__cx, f__cy, tau__u)

else 9999999

end if

end proc;


Here is my plot request:


Explore(implicitplot3d('yield(sigma__x, sigma__y, tau__xy, sigma__cx, sigma__cy, f__45, f__cx, f__cy, tau__u, f__tx, f__ty, alpha)' = 0, sigma__x = -10 .. 10, sigma__y = -10 .. 10, tau__xy = 0 .. 10, style = surfacecontour, numpoints = 100000, axes = normal), parameters = [f__cx = 0.1e-3 .. 10, f__cy = 0.1e-3 .. 10, f__45 = 0.1e-3 .. 10, sigma__cx = 0.1e-3 .. 10, sigma__cy = 0.1e-3 .. 10, tau__u = 0.1e-3 .. 10, f__tx = 0.1e-3 .. 10, f__ty = 0.1e-3 .. 10, alpha = 0.1e-3 .. 10]

 and this is what i get:

plot

The grainy surface should not be there. If it's not possible to remove it, it would be alright that surface would be smooth. Any ideas?


Hello people in mapleprimes,

 

I tried to solve y=x^3 for x, expecting of getting a result of x^(1/3),

through using restart;assume(x::real,y::real);
b:=y=x^3;
solve(b,x);

But, the result was:

Warning, solve may be ignoring assumptions on the input variables.
             (1/3)    1  (1/3)   1    (1/2)  (1/3)  
            y     , - - y      + - I 3      y     ,
                      2          2                  

                1  (1/3)   1    (1/2)  (1/3)
              - - y      - - I 3      y     
                2          2                

.

It means that solve couldn't use the assumption of x and y being real.

On the other hand, reading RealDomain package, y^(1/3) is returned properly:

 

with(RealDomain):
solve(b,x);
                              (1/3)
                             y     

What I want to ask you is

Aren't there ways other than using the RealDomain package, to obtain the solution of y^(1/3)?

 

I will be very glad if you give me answers.

 

Best wishes.

taro

Hello everyone,
I would like to get a symbolic result of each variable x,y and z for the following 3 nonlinear equations. Maple does not respond to the following code at all. (Not even an error report.)

restart;

eq1 := x^2+y^2+z^2-134*x+800*y-360*z+31489, 2;
eq2 := x^2+y^2+z^2-934*x+900*y-370*z+321789, 2;
eq3 := x^2+y^2+z^2-614*x+1350*y-1110*z+70048, 97;
solve({eq1, eq2, eq3}, {x, y, z});

Thanks in advance.

P.S: Afterwards my intention is to solve these equaitons numerically for different variable values, and transfer to MatLab in order to plot animations and graphs. 

I am a new user with Maple, and was using it as a documentation. But, can't fully see the file created a day before. 

The file opens but most of the content is gone and gives the error message.

There were problems during the loading process, Your worksheet may become incomplete

Googled a bit yet couldn't solve it :/ 

Is there any way to fix this?

Why_Mcausal_not_helping.mw

 

 

 

 

In plots made with 'complexplot3d', Maple uses by default a color wheel for the argument of complex numbers in which positive numbers are painted cyan and negative numbers are red. Is there a way to change this to the other common convention (i.e. cyan negative and red positive numbers)?

 

Any help would be really appreciated, as it's not convenient to have graphs made with different conventions in the same document and I wouldn't want to remake all the ones I already have.

I want to reference the previous equation/expression which is not displayed (':')in my worksheet. I allready know the '%' sign, but this references the previous equation/expression which was executed . By previous I mean the result (which is not displayed) in the previous line.

As I do not want the previous equation to be displayed I also cannot use the equation lable (CTRL+L).

 

Example

x:=a=b+1:

solve(previous,{b});

 

Thank you for your help.

I'm new here, so I'm not totally sure this is the right place to ask this. I apologize if it isn't, please let me know in that case.

 

My problem is that Maple won't recognize the built-in command 'complexplot3d'. For example, typing:

complexplot3d(z^2, z = -1-I .. 1+I)

doesn't do anything, and it's displayed again in blue as if it was not a command.

 

Any kind of help would be extremely helpful, as I have no clue of what's going on. Thanks in advance!

Hello people in mapleprimes

In the help of parse, there is the following example.

I could not understand why the first one is 4, and next 4^2, and the last 4^3 appeared, there.

Please tell me the way n is increased with the output taking 4, 4^2 and 4^3 sequentially in this example.

n := 0;
                             n := 0
input := "a := 4; a^2; a^3;";
                  input := "a := 4; a^2; a^3;"
parse(input,'lastread'='n','offset'=n,statement);
                               4
parse(input,'lastread'='n','offset'=n,statement);
                               16
parse(input,'lastread'='n','offset'=n,statement);
                               64

I know that it is written in the help that lastread shows the next unparsed character,

with the offset the next statement.

Thanks in advance

taro

how to compute Igusa invariant in maple?

why it is not included in maple?

how i can calculate roots of the characteristic polynomial equations {dsys and dsys2}
and dsolve them with arbitrary initial condition for differennt amont of m and n?
thanks
Kr.mw

restart; a := 1; b := 2; Number := 10; q := 1; omega := 0.2e-1
``

Q1 := besselj(0, xi*b)*(eval(diff(bessely(0, xi*r), r), r = a))-(eval(diff(besselj(0, xi*r), r), r = a))*bessely(0, xi*b):

J := 0:

m := 0:

U1 := (int(r*K1[m]*(diff(K_01[m], r)+K_01[m]/r), r = a .. b))/(int(r*K1[m]^2, r = a .. b)); -1; U2 := -(int(r*K_01[m]*(diff(K1[m], r)), r = a .. b))/(int(r*K_01[m]^2, r = a .. b)); -1; U3 := (int(r^2*omega^2*K_01[m], r = a .. b))/(int(r*K_01[m]^2, r = a .. b))

0.6222222222e-3/K_01[12]

(1)

Q2 := besselj(1, eta*b)*(eval(diff(bessely(1, eta*r), r), r = a))-(eval(diff(besselj(1, eta*r), r), r = a))*bessely(1, eta*b):

E2 := unapply(Q2, eta):

m := 0:

 
dsys := {diff(S_mn(t), t, t, t)+xi[m]^2*(diff(S_mn(t), t, t))+(-U1*U2+eta__n^2)*(diff(S_mn(t), t))+xi[m]^2*eta__n^2*S_mn(t) = -(2*U2*b_m/(Pi*xi[m])*(-besselj(0, xi[m]*b)/besselj(1, xi[m]*a)))*q+xi[m]^2*U3}; 1; dsolve(dsys)

{S_mn(t) = (3111111111/5000000000000)/(K_01[12]*eta__n^2)+_C1*cos(eta__n*t)+_C2*sin(eta__n*t)+_C3*exp(-xi[12]^2*t)}

(2)

dsys2 := {diff(Q_mn(t), t, t, t)+xi[m]^2*(diff(Q_mn(t), t, t))+(-U1*U2+eta__n^2)*(diff(Q_mn(t), t))+xi[m]^2*eta__n^2*Q_mn(t) = -2*besselj(0, xi[m]*b)*U1*U2*b_m*(1-exp(-xi[m]^2*t))/(besselj(1, xi[m]*a)*Pi*xi[m]^3)}; 1; dsolve(dsys2)

{Q_mn(t) = _C1*exp(-xi[12]^2*t)+_C2*sin(eta__n*t)+_C3*cos(eta__n*t)}

(3)

``

 

``



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