Maple 2019 Questions and Posts

These are Posts and Questions associated with the product, Maple 2019

Hi,

It seems that plottools:-extrude doesn't support the "style" option: no error returned, just the extusion being always of surface style.
Am I correct ?

The solver seems to have a problem with some sets of boundary conditions. (See attached worksheet.)

Is there a way to get this numerical solution?
 

BC_test.mw

[differentiation of f and greek letter xi in bracket]

Hi,

I am trying to find q(t) from this 

ode1:=-diff(q(t), t) - 1.851851852*10^(-7)*q(t)*(2.042885233*10^10 - 3.517396152*10^18*(0.00001474262739*cos((1000*sqrt(1122)*t)/33) + 0.00001474262739*sin((1000*sqrt(1122)*t)/33))^2) + 9.259259260*10^(-7);

with initial condition

ics := q(0) = 2.45*10^(-12)

using

dsolve({ode1,ics})

but I cannot get the full solution. Is there any way I could find q(t)?

Thanks,

Baharm31

This is the source:

ode1.mw

 

 

 

Hello 

I am having equation y(x) in 5 variable c1, c2, A, R and x.

I am not able to plot graph in x and y(x) for A=1, c1 = 2.3, c2 = 2.4 and R=0,2 5,9.

Range of x: -1..1

Caption :graph of y(x) at different value of R.

Legend: R=0, R=1, R=2, R=3.

my equation is


 

"y(x):=0.0000148809523809523809 A^3 R^2 x^10-0.000334821428571428572 A^3 R^2 x^8+0.00156250000000000000 A^3 R^2 x^7+0.000133928571428571429 A^3 R^2 x^6-0.00312500000000000000 A^2 R^2 x^7+0.00156250000000000000 A^3 R^2 x^5-0.0156250000000000000 A^3 R^2 x^4-0.00312500000000000000 A^2 R^2 x^5-0.00625000000000000000 A^2 R x^6+0.00647321428571428572 A^3 R^2 x^3+0.0625000000000000000 A^2 R^2 x^4-0.0129464285714285714 A^2 R^2 x^3-0.0625000000000000000 A R^2 x^4+0.0625000000000000000 A c1 c2 x^4+0.125000000000000000 A^2 R x^3-0.00319293058132343847 A^3 R^2+0.00803571428571428571 A^2 R x^2-0.250000000000000000 A R x^3+0.0125000000000000000 A^2 R^2-0.00178571428571428571 A^2 R-0.0125000000000000000 A R^2+0.0125000000000000000 A c1 c2-0.750000000000000000 A x^2+0.500000000000000001 (0.0380078849721706865 A^3 R^2-0.150000000000000000 A^2 R^2+0.150000000000000000 A R^2-0.150000000000000000 A c1 c2) x^2+0.750000000000000000 A+1.00000000000000000 (-0.00959821428571428571 A^3 R^2+0.0191964285714285714 A^2 R^2) x+1.00000000000000000 (-0.125000000000000000 A^2 R+0.250000000000000000 A R) x:"

``


 

Download Ques1.mw


 

NULL

Restart:

pde := diff(w(x, t), x $ 4) + diff(w(x, t), t $ 2)/c^2 = 0;

diff(diff(diff(diff(w(x, t), x), x), x), x)+(diff(diff(w(x, t), t), t))/c^2 = 0

(1)

test1 := w(x, t) = W(x)*cos(omega*t); pde1 := expand((eval(pde, test1))/cos(omega*t))

w(x, t) = W(x)*cos(omega*t)

 

diff(diff(diff(diff(W(x), x), x), x), x)-W(x)*omega^2/c^2 = 0

(2)

ode := algsubs(omega^2/c^2 = alpha^4, pde1); sol := dsolve(ode); sol := convert(sol, trig)

-W(x)*alpha^4+diff(diff(diff(diff(W(x), x), x), x), x) = 0

 

W(x) = _C1*exp(-alpha*x)+_C2*exp(alpha*x)+_C3*sin(alpha*x)+_C4*cos(alpha*x)

 

W(x) = _C1*(cosh(alpha*x)-sinh(alpha*x))+_C2*(cosh(alpha*x)+sinh(alpha*x))+_C3*sin(alpha*x)+_C4*cos(alpha*x)

(3)

L_collection := [indets(sol, specfunc({cos, cosh, sin, sinh}))[]]

[cos(alpha*x), cosh(alpha*x), sin(alpha*x), sinh(alpha*x)]

(4)

``

temp := collect(sol, [sinh, cosh, sin, cos])

W(x) = (-_C1+_C2)*sinh(alpha*x)+(_C1+_C2)*cosh(alpha*x)+_C3*sin(alpha*x)+_C4*cos(alpha*x)

(5)

CL := [coeffs(rhs(temp), L_collection)]NULL

[-_C1+_C2, _C1+_C2, _C3, _C4]

(6)

R:=[seq(cat(_D,i)=CL[i], i=1..nops(CL))]

[_D1 = -_C1+_C2, _D2 = _C1+_C2, _D3 = _C3, _D4 = _C4]

(7)

MX:= subs((rhs=lhs)~(R), temp);

W(x) = _D1*sinh(alpha*x)+_D2*cosh(alpha*x)+_D3*sin(alpha*x)+_D4*cos(alpha*x)

(8)

boundary_condition_1 := simplify(rhs(eval(diff(MX, `$`(x, 1)), x = 0))/alpha = 0)

_D1+_D3 = 0

(9)

boundary_condition_2 := simplify(rhs(eval(MX, x = 0)) = 0)

_D2+_D4 = 0

(10)

boundary_condition_3 := simplify(rhs(eval(diff(MX, `$`(x, 1)), x = L))/alpha = 0)

cosh(alpha*L)*_D1+sinh(alpha*L)*_D2+cos(alpha*L)*_D3-sin(alpha*L)*_D4 = 0

(11)

boundary_condition_4 := simplify(rhs(eval(MX, x = L)) = 0)

_D1*sinh(alpha*L)+_D2*cosh(alpha*L)+_D3*sin(alpha*L)+_D4*cos(alpha*L) = 0

(12)

boundary_condition_solve := solve([boundary_condition_1, boundary_condition_2, boundary_condition_3, boundary_condition_4]); MX := eval(MX, boundary_condition_solve)

Warning, solutions may have been lost

 

{L = L, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = 0}, {L = 0, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = alpha}, {L = L, _D1 = 0, _D2 = 0, _D3 = 0, _D4 = 0, alpha = alpha}

 

Error, invalid input: eval received ({L = L, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = 0}, {L = 0, _D1 = -_D3, _D2 = -_D4, _D3 = _D3, _D4 = _D4, alpha = alpha}, {L = L, _D1 = 0, _D2 = 0, _D3 = 0, _D4 = 0, alpha = alpha}), which is not valid for its 2nd argument, eqns

 

``


 

Download Free_Vibration_Euler_Bernouli_Beam_1.mw

I have tried to solve these 4 equations to get the characteristic equation and finally the solution of the PDE.  But it shows some error. Can you please help with this issue?

I am trying to use this command

plot({0, 2*x^2, 2*x^2 - 2*x^3 + 8/3*x^4 - 4*x^5}, x = -10 .. 10, color = ["DarkGreen", "CornflowerBlue", "Burgundy"])

However, only the last function is showing up. 0 and 2x^2 is not showing up. I can't change the axes sizes because then the last function disappears.

I have the following question, plot the graph of mu=5*log_10(D_L/10) where D_L=(c/H_0)*\int_0^z dz'/[A(1+z')^4+B(1+z)^3+C]^{1/2} with resepct to z, where A,B,C are numerical values given beforehand, and c is the speed of light and H_0 is the current Hubble constant.

 

Can someone please help with this simple plotting assignment.

 

Thanks, just by experience, can I learnt these syntax languages.

 

Peace out!

 

restart;
PDEtools[declare](f(x), prime = x);
N := 4;
f(x) :=  sum(p^i*f[i](x), i = 0..N):
HPMEq := (1 - p)*diff(f(x), x $ 3) + p*(diff(f(x), x $ 3) + 1/2*diff(f(x), x, x)*f(x));
for i from 0 to N do
    equ[1][i] := coeff(HPMEq, p, i) = 0;
end do;
cond[1][0] := f[0](0) = 0, D(f[0])(0) = 0, D(f[0])(5) = 1

for j to N do
    cond[1][j] := f[j](0) = 0, D(f[j])(0) = 0, D(f[j])(5) = 0;
end do

for i from 0 to N do
    dsolve({cond[1][i], equ[1][i]}, f[i](x));
    f[i](x) := rhs(%);
end do;
f(x) := evalf(simplify(sum(f[n](x), n = 0 .. N)))

convert(f(x), 'rational')

subs(x = 2.4, diff(f(x), x))

Prime_Derivative_Notation_for_Explicit_X_Values.mwPrime_Derivative_Notation_for_Explicit_X_Values.mw

## I hope this works. I can't seem to paste my MW file in this window in a readable format.

Hello all

could anyone tell how to solve following nonliner equations numerically.

f '''' - c1(g'') + R(f ' f '' - f f ''' )=0

g'' + c2(f '' -2g) -c3(f g' - f ' g)=0

f ' (-1)=0,   f ' (1)=0,   f(-1)=1-A, F(1) =1, g(-1)=0, g(1)=0

c1=3.2, c2=3.3, c3=3.4, R= -10 and A=1.6 are constants.   

please help to find solution  numerically and how to plot. 

Thanks in advence

 

I'm trying to arrange the constant terms of W(x). Like sinh (alpha*x) *(C2-C1).....and by defining C2-C1= D2 I want to rearrange the equation. Without this step, I'm not able to solve the equation further. I have also tried a few steps but it's not working.

Hello guys I do not have a Code for you I'm sorry for that. Mybe you can help me with my Task its in German but I need to find out the (x;y) for my Saddle Point and also the local Maxima (x;y). I hope you can help me. 

I am experimenting with using units especially for when there are awkard conversion factors. 

The document is for motor gearbox torques inertia ration and frequency.

I have documented my specific questions in the worksheet.

I am interested is see different ways of setting this up. Like I would rather setup the formulas at the start, then supply figures.


 

restart

``

with(Units[Natural])

UseSystem('SI')

UseSystem(SI)

(1)

Can I set the units for mass, accel, etc. so I don't have to re enter the default units if I change the figures later?

``

Mass := 3000*'kg'

3000*Units:-Unit(kg)

(2)

Accel := 1.5*'m'/'s'^2

1.5*Units:-Unit(m/s^2)

(3)

Rat := 5

5

(4)

``

Radius := (1/2)*(0.8282e-1-0.6e-2)*'m'

0.3841000000e-1*Units:-Unit(m)

(5)

Torque := Mass*Accel*Radius

172.8450000*Units:-Unit(J)

(6)

````

MotorTorque := Torque/Rat

34.56900000*Units:-Unit(J)

(7)

Jload := Mass*Radius^2

4.425984300*Units:-Unit(kg*m^2)

(8)

Jmtr := 1.42*10^(-2)*'kg'*'m'^2

0.1420000000e-1*Units:-Unit(kg*m^2)

(9)

Parse:-ConvertTo1D, "first argument to _Inert_ASSIGN must be assignable"

12.46756141

(10)

stiff := convert(48, 'units', 'N'*'m(radius)'/'arcmin', 'N'*'m(rarius)'/'rad', 'symbolic')

518400/Pi

(11)

/rad

518400/Pi

(12)

"(->)"

0.16501e6

(13)

``

Freq := sqrt(stiff/Jload)/(2*Pi)/s   i.e. Hertz

30.73072153*Units:-Unit(1/(kg^(1/2)*m))

(14)

stiff := 4567

4567

(15)

Freq

30.73072153*Units:-Unit(1/(kg^(1/2)*m))

(16)

``


 

Download Units_questions.mw

I have this problem, that maple wont isolate for x_1. I want to automate the prosses of any funktion, but how come it not work?

Hope you can help 

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