mehdi jafari

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These are questions asked by mehdi jafari

i have two equations;i.g eq1 and eq2. i want to factor psi(x,t) in eq2 using linear differential operators and substitute it in equation 1. could anyone help?


 

restart:with(DEtools):

eq1:=E*D(II)(x)*D[1](psi)(x,t)+E*II(x)*(D[1]@@2)(psi)(x,t)-G*A(x)*psi(x,t)+G*A(x)*D[1](v)(x,t)

E*(D(II))(x)*(D[1](psi))(x, t)+E*II(x)*(D[1, 1](psi))(x, t)-G*A(x)*psi(x, t)+G*A(x)*(D[1](v))(x, t)

(1)

convert(eq1,diff)

E*(diff(II(x), x))*(diff(psi(x, t), x))+E*II(x)*(diff(diff(psi(x, t), x), x))-G*A(x)*psi(x, t)+G*A(x)*(diff(v(x, t), x))

(2)

eq2:=-(G*D[1](A)(x)*psi(x,t)+G*A(x)*D[1](psi)(x,t))+(G*D[1](A)(x)*v(x,t))+G*A(x)*(D[1]@@2)(v)(x,t)-m(x)/G*D[2](v)(x,t)

-G*(D(A))(x)*psi(x, t)-G*A(x)*(D[1](psi))(x, t)+G*(D(A))(x)*v(x, t)+G*A(x)*(D[1, 1](v))(x, t)-m(x)*(D[2](v))(x, t)/G

(3)

convert(%,diff)

-G*(diff(A(x), x))*psi(x, t)-G*A(x)*(diff(psi(x, t), x))+G*(diff(A(x), x))*v(x, t)+G*A(x)*(diff(diff(v(x, t), x), x))-m(x)*(diff(v(x, t), t))/G

(4)

isolate(convert(eq2,diff),psi)

psi = (proc (x, t) options operator, arrow; -(G^2*A(x)*(diff(psi(x, t), x))-G^2*(diff(A(x), x))*v(x, t)-G^2*A(x)*(diff(diff(v(x, t), x), x))+m(x)*(diff(v(x, t), t)))/(G^2*(diff(A(x), x))) end proc)

(5)

eval(eq1,psi(x,t)=rhs((isolate(eq2,psi))(x,t))):convert(%,diff)

E*(diff(II(x), x))*(diff(psi(x, t), x))+E*II(x)*(diff(diff(psi(x, t), x), x))+A(x)*(G^2*A(x)*(diff(_XX(x, t), x))-G^2*A(x)*(diff(diff(v(x, t), x), x))-G^2*(diff(A(x), x))*v(x, t)+m(x)*(diff(v(x, t), t)))/(G*(diff(A(x), x)))+G*A(x)*(diff(v(x, t), x))

(6)

 

 

 


 

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I have a question? from the link: https://www.maplesoft.com/applications/view.aspx?SID=5084&view=html

How can we solve equation 2.1 to achieve solution 3.1 with boundary conditions explained in section " 1) Gaussian solution " ?
is this possible with maple?

Download pdsolve.mw

 

how this integration can be computed and plotted? tnx in advance

 

restart:Digits:=20:

T := 10^(-6);
delta := 10;
m := 1;
alpha:= 75/10;
v := 65;
mu := 8;

1/1000000

 

10

 

1

 

15/2

 

65

 

8

(1)

z := sqrt((omega^2 - 4*m^2)/alpha^2 - v^2/alpha^2*(4 *delta/alpha*tan(theta)^2 - v^4/alpha^4*tan(theta)^4))

(2/135)*(81*omega^2-324-1825200*tan(theta)^2+1930723600*tan(theta)^4)^(1/2)

(2)

a := sec(theta)/sqrt(2)*sqrt((2 *delta)/alpha - v^2/alpha^2*tan(theta)^2 + z)

(1/90)*sec(theta)*2^(1/2)*(5400-152100*tan(theta)^2+30*(81*omega^2-324-1825200*tan(theta)^2+1930723600*tan(theta)^4)^(1/2))^(1/2)

(3)

f1 := 1/(exp(( omega/2 - mu)/T) + 1);
f2 := 1/(exp((- (omega/2) - mu)/T) + 1);

1/(exp(500000*omega-8000000)+1)

 

1/(exp(-500000*omega-8000000)+1)

(4)

A1 := evalf(-(f1 - f2)*abs(omega/(4*a*alpha*cos(theta)^2*(-delta+ a^2 *alpha* cos(theta)^2) + 2*a*v^2*sin(theta)^2 + 1/10000)))

-1.*(1/(exp(500000.*omega-8000000.)+1.)-1./(exp(-500000.*omega-8000000.)+1.))*abs(omega/(.47140452079103168293*sec(theta)*(5400.-152100.*tan(theta)^2+30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*cos(theta)^2*(-10.+0.18518518518518518519e-2*sec(theta)^2*(5400.-152100.*tan(theta)^2+30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))*cos(theta)^2)+132.77894002280725736*sec(theta)*(5400.-152100.*tan(theta)^2+30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*sin(theta)^2+0.10000000000000000000e-3))

(5)

b := sec(theta)/sqrt(2)*sqrt((2*delta)/alpha - v^2/alpha^2*tan(theta)^2 - z)

(1/90)*sec(theta)*2^(1/2)*(5400-152100*tan(theta)^2-30*(81*omega^2-324-1825200*tan(theta)^2+1930723600*tan(theta)^4)^(1/2))^(1/2)

(6)

f3 := 1/(exp(( omega/2 - mu)/T) + 1);
f4 := 1/(exp((- (omega/2) - mu)/T) + 1);

1/(exp(500000*omega-8000000)+1)

 

1/(exp(-500000*omega-8000000)+1)

(7)

A2 := evalf(-(f3 - f2)*abs(omega/(4*b*alpha*cos(theta)^2*(-delta+ b^2 *alpha* cos(theta)^2) + 2*b*v^2*sin(theta)^2 + 1/10000)))

-1.*(1/(exp(500000.*omega-8000000.)+1.)-1./(exp(-500000.*omega-8000000.)+1.))*abs(omega/(.47140452079103168293*sec(theta)*(5400.-152100.*tan(theta)^2-30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*cos(theta)^2*(-10.+0.18518518518518518519e-2*sec(theta)^2*(5400.-152100.*tan(theta)^2-30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))*cos(theta)^2)+132.77894002280725736*sec(theta)*(5400.-152100.*tan(theta)^2-30.*(81.*omega^2-324.-1825200.*tan(theta)^2+1930723600.*tan(theta)^4)^(1/2))^(1/2)*sin(theta)^2+0.10000000000000000000e-3))

(8)

plot(int(A1+A2,theta=0..2*Pi),omega=0..50);

Warning,  computation interrupted

 

 


 

Download code.mw

How can this expression sorted in order of the symbol "y"? I want the terms with y locate at the beginnig.
 

restart:

f:=x^2+x^y+1-z

x^2+x^y+1-z

(1)

 


 

Download sort.mw

 

I want to find all roots of an function.we think there maybe 35 roots, but the commands


1. "SolveEquations" gives us 26 roots,

2."fsolve" gives us 10 roots,

3."Student[Calculus1]:-Roots" gives us 29 roots,

4.the proc "findroots" written by @acer 6 to 10 roots.

 I have tried everything but i cannot find all roots, what is th problem?
can anyone help?how many roots are there? and how to find all of them?

problem.mw

EDIT: the uploaded file is edited.

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