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Still cannot get the exact solution...

Sofey 10
May 03 2015
0 0

@Mac Dude 

i already not using simplify, but still cannot get the solution that i want to prove.

Here i state the solution utt-uxx+u+u3=(x2-2)cosh(x+t)-4sinh(x+t)+x6cosh3(x+t)


restart

eqn1 := u+(1-exp(-m))*u[t]+(1-exp(-m))^2*u[tt]/factorial(2)+(u-(1-exp(-m))*u[t]+(1-exp(-m))^2*u[tt]/factorial(2))-u-(1-exp(-m))*u[x]-(1-exp(-m))^2*u[xx]/factorial(2)-u+(1-exp(-m))*u[x]-(1-exp(-m))^2*u[xx]/factorial(2)+(1-exp(-m))^2*u+(1-exp(-m))^2*u^3-(1-exp(-m))^2*(4*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+(t+1-exp(-m)))-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+(t+1-exp(-m)))+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+(t+1-exp(-m)))^3))*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)/((((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+(t+1-exp(-m)))-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+(t+1-exp(-m)))+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+(t+1-exp(-m)))^3)*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3+(x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)+(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+(t+1-exp(-m)))-(4*(x+1-exp(-m)))*sinh(x+1-exp(-m)+(t+1-exp(-m)))+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+(t+1-exp(-m)))^3+(x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3));

(1-exp(-m))^2*u[tt]-(1-exp(-m))^2*u[xx]+(1-exp(-m))^2*u+(1-exp(-m))^2*u^3-(1-exp(-m))^2*(4*((x+1-exp(-m))^2-2)*cosh(x+2-2*exp(-m)+t)-16*(x+1-exp(-m))*sinh(x+2-2*exp(-m)+t)+4*(x+1-exp(-m))^6*cosh(x+2-2*exp(-m)+t)^3)*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)/((((x+1-exp(-m))^2-2)*cosh(x+2-2*exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+2-2*exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+2-2*exp(-m)+t)^3)*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3+(x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)+(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+2-2*exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+2-2*exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+2-2*exp(-m)+t)^3+(x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3))

 (1)

``

b := eqn1/(1-exp(-m))^2;

((1-exp(-m))^2*u[tt]-(1-exp(-m))^2*u[xx]+(1-exp(-m))^2*u+(1-exp(-m))^2*u^3-(1-exp(-m))^2*(4*((x+1-exp(-m))^2-2)*cosh(x+2-2*exp(-m)+t)-16*(x+1-exp(-m))*sinh(x+2-2*exp(-m)+t)+4*(x+1-exp(-m))^6*cosh(x+2-2*exp(-m)+t)^3)*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)/((((x+1-exp(-m))^2-2)*cosh(x+2-2*exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+2-2*exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+2-2*exp(-m)+t)^3)*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3+(x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)+(((x+1-exp(-m))^2-2)*cosh(x+1-exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+1-exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+1-exp(-m)+t)^3)*((x^2-2)*cosh(x+1-exp(-m)+t)-4*x*sinh(x+1-exp(-m)+t)+x^6*cosh(x+1-exp(-m)+t)^3)*(((x+1-exp(-m))^2-2)*cosh(x+2-2*exp(-m)+t)-4*(x+1-exp(-m))*sinh(x+2-2*exp(-m)+t)+(x+1-exp(-m))^6*cosh(x+2-2*exp(-m)+t)^3+(x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)))/(1-exp(-m))^2

 (2)

c := subs(m = 0, b);

((1-exp(0))^2*u[tt]-(1-exp(0))^2*u[xx]+(1-exp(0))^2*u+(1-exp(0))^2*u^3-(1-exp(0))^2*(4*((x+1-exp(0))^2-2)*cosh(x+2-2*exp(0)+t)-16*(x+1-exp(0))*sinh(x+2-2*exp(0)+t)+4*(x+1-exp(0))^6*cosh(x+2-2*exp(0)+t)^3)*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(0))^2-2)*cosh(x+1-exp(0)+t)-4*(x+1-exp(0))*sinh(x+1-exp(0)+t)+x^6*cosh(x+1-exp(0)+t)^3)*((x^2-2)*cosh(x+1-exp(0)+t)-4*x*sinh(x+1-exp(0)+t)+x^6*cosh(x+1-exp(0)+t)^3)/((((x+1-exp(0))^2-2)*cosh(x+2-2*exp(0)+t)-4*(x+1-exp(0))*sinh(x+2-2*exp(0)+t)+(x+1-exp(0))^6*cosh(x+2-2*exp(0)+t)^3)*((x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)*(((x+1-exp(0))^2-2)*cosh(x+1-exp(0)+t)-4*(x+1-exp(0))*sinh(x+1-exp(0)+t)+(x+1-exp(0))^6*cosh(x+1-exp(0)+t)^3+(x^2-2)*cosh(x+1-exp(0)+t)-4*x*sinh(x+1-exp(0)+t)+x^6*cosh(x+1-exp(0)+t)^3)+(((x+1-exp(0))^2-2)*cosh(x+1-exp(0)+t)-4*(x+1-exp(0))*sinh(x+1-exp(0)+t)+(x+1-exp(0))^6*cosh(x+1-exp(0)+t)^3)*((x^2-2)*cosh(x+1-exp(0)+t)-4*x*sinh(x+1-exp(0)+t)+x^6*cosh(x+1-exp(0)+t)^3)*(((x+1-exp(0))^2-2)*cosh(x+2-2*exp(0)+t)-4*(x+1-exp(0))*sinh(x+2-2*exp(0)+t)+(x+1-exp(0))^6*cosh(x+2-2*exp(0)+t)^3+(x^2-2)*cosh(x+t)-4*x*sinh(x+t)+x^6*cosh(x+t)^3)))/(1-exp(0))^2

 (3)

d := simplify(c)

Error, numeric exception: division by zero

  

``


Download consistency_expmle_4.mw

Thank you...

Sofey 10
May 01 2015
0 0

@Rouben Rostamian  

Thank you for your help. its work. I already add with(plots) to my complexplot3d.

Thank you...

Sofey 10
May 01 2015
0 0

@Preben Alsholm

Thank you for your help.. i already add the thickness =3 and change the complexplot ({0,1+I,1-I}) to the command. its work. I acctually try to plot the graph for stability region for my problems. 

@Carl Love  ow i see.. that is my m...

Sofey 10
May 01 2015
0 0

@Carl Love  ow i see.. that is my mistake.. thanks for your help.

numeric...

Sofey 10
November 05 2012
0 0

ok,, tq very much Mr Adri vanderMeer van der Meer.. before this i have tried use numeric, but the graph still do not want to out.. Thank you again for helping me.. 

numeric...

Sofey 10
November 05 2012

ok,, tq very much Mr Adri vanderMeer van der Meer.. before this i have tried use numeric, but the graph still do not want to out.. Thank you again for helping me.. 

Yes,, this is that i want.. TQ so much.....

Sofey 10
November 02 2012
0 0

Yes,, this is that i want.. TQ so much..

Yes,, this is that i want.. TQ so much.....

Sofey 10
November 02 2012

Yes,, this is that i want.. TQ so much..

@Adri vanderMeer van der Meer i wan...

Sofey 10
November 02 2012
0 0

@Adri vanderMeer van der Meer i want to plot graph for three story building due to the effect of earthquake.. can u hepl me?

@Adri vanderMeer van der Meer i wan...

Sofey 10
November 02 2012

@Adri vanderMeer van der Meer i want to plot graph for three story building due to the effect of earthquake.. can u hepl me?

this is my worksheet.. ...

Sofey 10
November 02 2012
0 0

this is my worksheet..


restart; with(plots); with(LinearAlgebra); with(linalg)

m1 := 2280; m2 := 2243; m3 := 2220; k1 := 300; k2 := 200; k3 := 100; F0 := 4.1; omega1 := sqrt((k1+k2)/m1); omega2 := sqrt((k2+k3)/m2); omega3 := sqrt(k3/m3)

Sys := m1*(diff(u1(t), t, t))+(k1+k2)*u1(t)-k2*u2(t) = F0*cos(omega1*t), m2*(diff(u2(t), t, t))-k2*u1(t)+(k2+k3)*u2(t)-k3*u3(t) = F0*cos(omega2*t), m3*(diff(u3(t), t, t))-k3*u2(t)+k3*u3(t) = F0*cos(omega3*t)

IC := u1(0) = 0, u2(0) = 0, u3(0) = 0, (D[1](u1))(0) = 0, (D[1](u2))(0) = 0, (D[1](u3))(0) = 0

csol := dsolve({IC, Sys}, {u1(t), u2(t), u3(t)})

p1 := subs(csol, u1(t))

p2 := subs(csol, u2(t))

p3 := subs(csol, u3(t))

plot([p1, p2, p3], t = 0 .. 50*Pi, color = [red, blue, green], thickness = [1, 1, 1], linestyle = [1, 1, 1], labels = ['t', 'u(t)'], title = "red=First Floor,blue=Second Floor,green=Third Floor")

  

NULL


Download Testing_2...mw

this is my worksheet.. ...

Sofey 10
November 02 2012

this is my worksheet..


restart; with(plots); with(LinearAlgebra); with(linalg)

m1 := 2280; m2 := 2243; m3 := 2220; k1 := 300; k2 := 200; k3 := 100; F0 := 4.1; omega1 := sqrt((k1+k2)/m1); omega2 := sqrt((k2+k3)/m2); omega3 := sqrt(k3/m3)

Sys := m1*(diff(u1(t), t, t))+(k1+k2)*u1(t)-k2*u2(t) = F0*cos(omega1*t), m2*(diff(u2(t), t, t))-k2*u1(t)+(k2+k3)*u2(t)-k3*u3(t) = F0*cos(omega2*t), m3*(diff(u3(t), t, t))-k3*u2(t)+k3*u3(t) = F0*cos(omega3*t)

IC := u1(0) = 0, u2(0) = 0, u3(0) = 0, (D[1](u1))(0) = 0, (D[1](u2))(0) = 0, (D[1](u3))(0) = 0

csol := dsolve({IC, Sys}, {u1(t), u2(t), u3(t)})

p1 := subs(csol, u1(t))

p2 := subs(csol, u2(t))

p3 := subs(csol, u3(t))

plot([p1, p2, p3], t = 0 .. 50*Pi, color = [red, blue, green], thickness = [1, 1, 1], linestyle = [1, 1, 1], labels = ['t', 'u(t)'], title = "red=First Floor,blue=Second Floor,green=Third Floor")

  

NULL


Download Testing_2...mw

TQ.. but actually, i want to plot the gr...

Sofey 10
November 02 2012
0 0

TQ.. but actually, i want to plot the graph for 3 systems ODE.. i dont want to used numeric.. my problems is on plotting command's.. can you help me?

TQ.. but actually, i want to plot the gr...

Sofey 10
November 02 2012

TQ.. but actually, i want to plot the graph for 3 systems ODE.. i dont want to used numeric.. my problems is on plotting command's.. can you help me?

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