MaplePrimes Questions

5_6190449716501677775.pdf

I ahve a signal y_a to which adding mu(t) doesn't seem to give any plot but error , what is missing here?.

And also in second k(x,t) pdf file I want the value of k(x,t) after I did the integration. When I type k(x,t) and hit enter it's not giving me the value of k(x,t) but returns k(x,t) as it is.K(x_t).pdf

I do not remember now if this was asked before. Doing search here is hard. 

But I am trying this now on 2022.1 and this gives FAIL.

What is the correct syntax to use odetest to verify solution to ode using series method with expansion around infinity? Why do I get FAIL here?
 

interface(version)

`Standard Worksheet Interface, Maple 2022.1, Windows 10, May 26 2022 Build ID 1619613`

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1257 and is the same as the version installed in this computer, created 2022, June 22, 16:27 hours Pacific Time.`

restart;

ode:=x^3*diff(y(x),x$2)+x^2*diff(y(x),x)+y(x)=0;
sol:=dsolve(ode,y(x),'series',x=infinity);
odetest(sol,ode,'series','point'=infinity)

x^3*(diff(diff(y(x), x), x))+x^2*(diff(y(x), x))+y(x) = 0

y(x) = _C1*(1-1/x+(1/4)/x^2-(1/36)/x^3+(1/576)/x^4-(1/14400)/x^5+O(1/x^6))+_C2*(ln(1/x)*(1-1/x+(1/4)/x^2-(1/36)/x^3+(1/576)/x^4-(1/14400)/x^5+O(1/x^6))+2/x-(3/4)/x^2+(11/108)/x^3-(25/3456)/x^4+(137/432000)/x^5+O(1/x^6))

Warning, unable to compute series necessary to test the given solution

FAIL

 


 

Download odetest_series.mw

Update

I've testsed methods given below on 6 random ode's using Maple odetest, VV method and Axel method. THis is the result obtained using Maple 2022.1 

odetest was able to verify the solution zero out of 6 times.
VV method was able to verify the solution 3 out of 6 times.
Axel method was able to verify the solution 5 out of 6 times.

So based on this small test, Axel method seems to do the best. Attached worksheet. I will use this method to verify my series solution to ode's instead of Maple's odetest but will use Maple's odetest for non-series method solutions.


 

interface(version);

`Standard Worksheet Interface, Maple 2022.1, Windows 10, May 26 2022 Build ID 1619613`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1257 and is the same as the version installed in this computer, created 2022, June 22, 16:27 hours Pacific Time.`

restart;

Example 1  Regular singular point. Complex roots

 

Order:=6;
ode:=sin(x)*diff(y(x),x$2)+cos(x)*diff(y(x),x)+1/x*y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0)

6

sin(x)*(diff(diff(y(x), x), x))+cos(x)*(diff(y(x), x))+y(x)/x = 0

y(x) = _C1*x^(-I)*(series(1+(1/48-(1/16)*I)*x^2+(1/57600-(217/57600)*I)*x^4+O(x^6),x,6))+_C2*x^I*(series(1+(1/48+(1/16)*I)*x^2+(1/57600+(217/57600)*I)*x^4+O(x^6),x,6))

VV method

 

odetest(sol,ode):
asympt(%,x);

Error, (in asympt) unable to compute series

odetest method

 

odetest(sol,ode,'series','point'=0);

y(x) = _C1*x^(-I)*(series(1+(1/48-(1/16)*I)*x^2+(1/57600-(217/57600)*I)*x^4+O(x^6),x,6))+_C2*x^I*(series(1+(1/48+(1/16)*I)*x^2+(1/57600+(217/57600)*I)*x^4+O(x^6),x,6))

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

 

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

Example 2 Regular singular point. Dierence is integer

 

Order:=6;
ode:=sin(x)*diff(y(x),x$2)+cos(x)*y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0):

6

sin(x)*(diff(diff(y(x), x), x))+cos(x)*y(x) = 0

VV method

 

odetest(sol,ode):
asympt(%,x);
convert(%,polynom);

O(x^7)

0

odetest method

 

odetest(sol,ode,'series','point'=0);

Warning, unable to compute series necessary to test the given solution

FAIL

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

   

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

Example 3 Regular singular point. Repeated root

 

Order:=6;
ode:=(exp(x)-1)*diff(y(x),x$2)+exp(x)*diff(y(x),x)+y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0):

6

(exp(x)-1)*(diff(diff(y(x), x), x))+exp(x)*(diff(y(x), x))+y(x) = 0

VV method

 

odetest(sol,ode):
asympt(%,x):
convert(%,polynom);

0

odetest method

 

odetest(sol,ode,'series','point'=0);

Warning, unable to compute series necessary to test the given solution

FAIL

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

   

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

Example 4 Regular singular point. Repeated root

 

Order:=6;  
ode:=(exp(x)-1)*diff(y(x),x$2)+exp(x)*diff(y(x),x)+y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0):

6

(exp(x)-1)*(diff(diff(y(x), x), x))+exp(x)*(diff(y(x), x))+y(x) = 0

VV method

 

odetest(sol,ode):
asympt(%,x):
convert(%,polynom);

0

odetest method

 

odetest(sol,ode,'series','point'=0);

Warning, unable to compute series necessary to test the given solution

FAIL

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

   

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

Example 5 . Regular singular point. Complex roots

 

Order:=6;  
ode:=x^3*diff(y(x),x$2)+sin(x^3)*diff(y(x),x)+x*y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0):

6

x^3*(diff(diff(y(x), x), x))+sin(x^3)*(diff(y(x), x))+x*y(x) = 0

VV method

 

odetest(sol,ode):
asympt(%,x);
#convert(%,polynom);

Error, (in asympt) unable to compute series

odetest method

 

odetest(sol,ode,'series','point'=0);

Error, (in odetest/series) need to determine the sign of I*3^(1/2)

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

   

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
#convert(%,polynom);

Error, (in MultiSeries:-multiseries) need to determine the sign of -I*3^(1/2)

Example 6 . Regular singular point. Complex roots

 

Order:=6;  
ode:=x^2*diff(y(x),x$2)+x*diff(y(x),x)+(x+1)*y(x)=0;
sol:=dsolve(ode,y(x),type='series',x=0):

6

x^2*(diff(diff(y(x), x), x))+x*(diff(y(x), x))+(x+1)*y(x) = 0

VV method

 

odetest(sol,ode):
asympt(%,x);
#convert(%,polynom);

Error, (in asympt) unable to compute series

odetest method

 

odetest(sol,ode,'series','point'=0);

y(x) = _C1*x^(-I)*(series(1+(-1/5-(2/5)*I)*x+(-1/40+(3/40)*I)*x^2+(3/520-(7/1560)*I)*x^3+(-1/2496+(1/12480)*I)*x^4+(9/603200+(1/361920)*I)*x^5+O(x^6),x,6))+_C2*x^I*(series(1+(-1/5+(2/5)*I)*x+(-1/40-(3/40)*I)*x^2+(3/520+(7/1560)*I)*x^3+(-1/2496-(1/12480)*I)*x^4+(9/603200-(1/361920)*I)*x^5+O(x^6),x,6))

y(t) = _C1*t^(-I)*(series(1+(1/48-(1/16)*I)*t^2+(1/57600-(217/57600)*I)*t^4+O(t^6),t,6))+_C2*t^I*(series(1+(1/48+(1/16)*I)*t^2+(1/57600+(217/57600)*I)*t^4+O(t^6),t,6))

Axel method

   

rhs(sol):
Y:= unapply(%, x):
eval(lhs(ode), y=Y):
MultiSeries:-asympt(%, x):
convert(%,polynom);

0

 

 


 

Download test_new_odetest.mw

 

 

 

What is the [explict] relation between Maple's WeierstrassP and Weierstrass' P-function (e.g. https://en.wikipedia.org/wiki/Weierstrass_elliptic_function) ?

How can I specify english units as the default in Flow?  Rather than Newtons (N), pound force (lbf)?

pdf.mw
 

with(stats)

"f(x):=statevalf[pdf,normald[0,2*4.47]]  "

proc (x) options operator, arrow, function_assign; statevalf[pdf, normald[0, 2*4.47]] end proc

(1)

plot(f(x), -20 .. 20)

 

int(x*f(x), x)

.5000000000*x^2*statevalf[pdf, normald[0, 8.94]]

(2)

NULL


 

Download pdf.mw

Want to integrate x*f(x) where x is from -20..20, I am expecting a pure float number but getting symbols like statevalf_pdf in answer.

 

I am using some custom procedures which return error messages if something doesn´t work as planned and would need to make a distinction (when using try..catch) between these errors and all the other potential error messages Maple can return. Is there a way to do this efficiently - without having to list all of the error messages from my own procedures after catch?

Hello Everyone;

Hope you are fine. My problem is convert into nonlinear system of ODE's and further i need make the code of apply rk-4 for the formulated ODE's. Kindly guide me. The file is attached. I am waiting for your kind response.

Thanks

Question3.mw

 


 

restart

``

var111 := [C[1, 1](t), C[1, 2](t), C[1, 3](t), C[2, 1](t), C[2, 2](t), C[2, 3](t), C[3, 1](t), C[3, 2](t), C[3, 3](t), ZETA[1](t), ZETA[2](t), ZETA[3](t)]:

sysM := [diff(C[1, 1](t), t) = -(3/16)*Pi*(C[2, 1](t)+4*C[1, 1](t)), diff(C[1, 2](t), t) = -5*Pi*(C[2, 2](t)+4*C[1, 2](t)), diff(C[1, 3](t), t) = -(945/4)*Pi*(C[2, 3](t)+4*C[1, 3](t)), diff(C[2, 1](t), t) = -(1/8)*Pi*(C[3, 1](t)+6*C[2, 1](t)+6*C[1, 1](t)), diff(C[2, 2](t), t) = -10.4719755119659774615421446110*C[3, 2](t)-62.8318530717958647692528676658*C[2, 2](t)-62.8318530717958647692528676658*C[1, 2](t)-2.38361014507273884349657421134*10^15*ZETA[1](t)*C[1, 1](t), diff(C[2, 3](t), t) = -494.800842940392435057866332869*C[3, 3](t)-2968.80505764235461034719799721*C[2, 3](t)-2968.80505764235461034719799721*C[1, 3](t)-1.35954060126371030332767566128*10^16*ZETA[1](t)*C[1, 2](t)-1.35954060126371030332767566128*10^16*ZETA[2](t)*C[1, 1](t), diff(C[3, 1](t), t) = -(3/8)*Pi*(2*C[3, 1](t)+3*C[2, 1](t)), diff(C[3, 2](t), t) = -62.8318530717958647692528676658*C[3, 2](t)-94.2477796076937971538793014986*C[2, 2](t)-1.12625579354686910355213131486*10^17*ZETA[1](t)*C[2, 1](t), diff(C[3, 3](t), t) = -2968.80505764235461034719799721*C[3, 3](t)-4453.20758646353191552079699581*C[2, 3](t)-6.42382934097103118322326749959*10^17*ZETA[1](t)*C[2, 2](t)-6.42382934097103118322326749959*10^17*ZETA[2](t)*C[2, 1](t), diff(ZETA[1](t), t) = -(1/3)*C[2, 1](t), diff(ZETA[2](t), t) = -(1/3)*C[2, 2](t), diff(ZETA[3](t), t) = -(1/3)*C[2, 3](t)]:

ICS := [C[1, 1] = 0.998238989835086492681507032141e-1, C[1, 2] = -0.137051161872492529218951625903e-1, C[1, 3] = -0.629146365720807620696267926206e-2, C[2, 1] = 0.923300332435106257640735267282e-1, C[2, 2] = -0.126762613568515069966837491839e-1, C[2, 3] = -0.581915808273854734025727975244e-2, C[3, 1] = -0.190143920352772604950256237747e-1, C[3, 2] = 0.261054171122321128306306984717e-2, C[3, 3] = 0.119839394846335068333097530793e-2, ZETA[1] = .464598743230343884242076682299, ZETA[2] = .429720916976380440572769663279, ZETA[3] = -0.884964696113332752036741498040e-1]:

``


 

Download Question3.mw

The worksheet here shows a couple of failed attempts at coaxing Maple to calculate the general solution of a pretty simple second order ODE.  I have also included the expected solution which I  have calculated by hand.  Perhaps I am missing a key trick.  Any ideas?

The ODE that I am actually interested in is significantly more complex. The one in the worksheet is a much simplified "bare bones" specimen that exhibits the issue that I am facing.

Attempt to solve with Heaviside

restart;

de := diff(u(x),x$2) = Heaviside(x - a)*u(x);

diff(diff(u(x), x), x) = Heaviside(x-a)*u(x)

dsolve fails:

dsolve(de);

u(x) = DESol({diff(diff(_Y(x), x), x)-Heaviside(x-a)*_Y(x)}, {_Y(x)})

Attempt to solve with piecewise

restart;

de := diff(u(x),x$2) = piecewise(x < a, 0, 1)*u(x);

de := diff(u(x), x, x) = piecewise(x < a, 0, 1)*u(x)

dsolve(de);

Error, (in dsolve) give the main variable as a second argument

dsolve(de, u(x));

Error, (in dsolve) give the main variable as a second argument

 

 

The solution is easy to calculate by hand

We just solve the (quite trivial) DE over the intervals x < a and x>a

separately, and patch the two solutions by requiring the continuity

of u(x) and diff(u(x), x) at x = a.  We get

sol := piecewise(x < a,
        x*c[1] + c[2],
        ((a*c[1] + c[1] + c[2])*exp(x))/(2*exp(a)) + ((a*c[1] - c[1] + c[2])*exp(-x))/(2*exp(-a)));

sol := piecewise(x < a, x*c[1]+c[2], (a*c[1]+c[1]+c[2])*exp(x)/(2*exp(a))+(a*c[1]-c[1]+c[2])*exp(-x)/(2*exp(-a)))

Download solving-an-ode.mw

Hello,

I am fairly new to Maple. Suppose I have two Matrices

A := <<true, false, true> | <true, false, true> | <false, false, false>>

B := <<1, 2, 6> | <3, 4, 7> | <22, 33, 44>>

and apply select(A, B)

Why do I receive [[[(),3,22],[(),(),()],[(),7,44]]] instead of [[[1,(),6],[3,(),7],[(),(),()]]] as a result? I just want to select every element of B where A is true.

I appreciate any insight.

This is a simple algebraic, but I would like to know how to officially solve the problem,

I tried factor(6*a+12*b+18*c); it simply outputs what I input.

I tried primpart(6*a+12*b+18*c) ; the output is: a+2b+3c

I tried content(6*a+12*b+18*c), the output is 6

What I'm looking for an output is, 6*(a+2*b+3*c), this is the answer my Algebra book is looking for, I also get this answer by

using my HP Graphing Calculator, but I'm unable to get the answer from Maples. Can anyone help?

Could you Please Help me,the Maple code for Plot this equations in any Numerical Method

restart

with(PDETools, declare):

with(LinearAlgebra):

with(PolynomialIdeals):

with(plots):

declare(f(x));

f(x)*`will now be displayed as`*f

(1)

eq1 := diff(f(x), x, x, x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[fl])*(eta*`cos&omega;`+f(x)*`sin&omega;`)*(diff(f(x), x, x))+(1-phi)^2.5*M*sin^2*alpha*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`&rho;&beta;`[s]/`&rho;&beta;`[fl])*lambda[T]*theta = 0;

diff(diff(diff(f(x), x), x), x)+(1/2)*(1-phi)^2.5*(1-phi+phi*rho[s]/rho[fl])*(eta*`cos&omega;`+f(x)*`sin&omega;`)*(diff(diff(f(x), x), x))+(1-phi)^2.5*M*sin^2*alpha*(1-(diff(f(x), x)))+(1-phi)^2.5*(1-phi+phi*`&rho;&beta;`[s]/`&rho;&beta;`[fl])*lambda[T]*theta = 0

(2)

eq2 := K[nf]*(diff(theta(x), x, x))/K[f]+(1/2)*Pr*(eta*`cos&omega;`+f*`sin&omega;`)*(diff(theta(x), x)) = 0;

K[nf]*(diff(diff(theta(x), x), x))/K[f]+(1/2)*Pr*(eta*`cos&omega;`+f*`sin&omega;`)*(diff(theta(x), x)) = 0

(3)

bcs := F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0;

F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0

(4)

a1 := [M = 1, alpha = 0, phi = 0.5e-1, `cos&omega;` = 1, `sin&omega;` = 1, sin(alpha) = 0, lambda[T] = 0, Pr = 6.2, rho[s] = 5200, rho[fl] = 997.1, `&rho;&beta;`[fl] = 20939.1, K[nf] = .6842, eta = 0];

[M = 1, alpha = 0, phi = 0.5e-1, `cos&omega;` = 1, `sin&omega;` = 1, sin(alpha) = 0, lambda[T] = 0, Pr = 6.2, rho[s] = 5200, rho[fl] = 997.1, `&rho;&beta;`[fl] = 20939.1, K[nf] = .6842, eta = 0]

 

[Pr = 6.2, M = 1, phi = 0.5e-1, `cos&omega;` = 1, `sin&omega;` = 1, sin(alpha) = 0, lambda[T] = 0, `&rho;&beta;`[fl] = 20939.1, K[nf] = .6842, K[f] = .613, eta = 0]

(5)

b1 := subs(a1, eq1);

diff(diff(diff(f(x), x), x), x)+.5325197465*f(x)*(diff(diff(f(x), x), x)) = 0

(6)

c1 := subs(a2, eq2);

1.116150082*(diff(diff(theta(x), x), x))+3.100000000*f*(diff(theta(x), x)) = 0

(7)

d1 := dsolve({b1, bcs}, {bcs, c1}, numeric); d1(0)

Error, (in dsolve/numeric/process_input) invalid argument: {1.116150082*(diff(diff(theta(x), x), x))+3.100000000*f*(diff(theta(x), x)) = 0, F(0) = 0, F(1) = 0, F(10) = 1, Theta(0) = 1, Theta(10) = 0}

 

d1(0)

(8)

``

Download  Numerical Method.mw

Inverse kinematics can be done in several ways (this webinar gives a very good overview https://www.youtube.com/watch?v=X0OZ9EM6dns). A effective and simple method is to run a model in reverse direction. This can’t be done with causal modeling tools, where information flow is fixed by design (https://de.maplesoft.com/support/help/MapleSim/view.aspx?path=MapleSimUserGuide/Chapter01).

Inverse kinematics, which is possible with acausal modeling tools, is only an example for running a model in the reverse (i.e., inverted) direction.

Without success, I tried to find a reference who first came up with that elegant approach.

Anyone knows more?

Hi

I have a problem with calculating complex numbers in Maple.

I type forexample 8(cos(Pi/2)+I*sin(Pi/2)) and I get 8, I should get 8I

Should I re-install Maple or edit my settings?

best regards

Hi everybody,how can I solve these equations in Maple and plot the answers? tnx...

eq1 := diff(x(t), t) = 35*(y-x)

eq2 := diff(y(t), t) = -x*z-7*x+28*y

eq3 := diff(z(t), t) = x*y-3*z

Hi Dear All,

 

I need to extract the coordinates from spacecurve commend. For example;

 

h3:=spacecurve([-x,-y,z],omega=ws..0,color=green,thickness=5):
h4:=spacecurve([-x,y,z],omega=ws..0,color=blue,thickness=5):

Where, omega is a parameter difinening x, y, z.

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