MaplePrimes Questions

restart;
deq1 := diff(u(x, y), x) - diff(u(x, y), y$2) = exp(x+y);
                              /  2         \             
              / d         \   | d          |             
      deq1 := |--- u(x, y)| - |---- u(x, y)| = exp(x + y)
              \ dx        /   |   2        |             
                              \ dy         /             

deq2 := diff(u(x, y), x) - diff(u(x, y), y$2) = exp(1)^(x+y);
                            /  2         \                  
            / d         \   | d          |           (x + y)
    deq2 := |--- u(x, y)| - |---- u(x, y)| = (exp(1))       
            \ dx        /   |   2        |                  
                            \ dy         /                  

pdsolve(deq1, u(x,y));  ### no result
pdsolve(deq2, u(x,y));
                        /                                        
                        |                                        
PDESolStrucApplyFunction|uApplyFunction(x,y)=_F1ApplyFunction(x)
                        \                                        

                        1
  _F2ApplyFunction(y) - -
                        2

                       x+y                                                                                   
  (expApplyFunction(1))    (_C1 expApplyFunction(uminus0y)+_C2 expApplyFunction(y)+_C3 expApplyFunction(y) y)
  -----------------------------------------------------------------------------------------------------------
                                            _C3 expApplyFunction(y)                                          

  ,[{diffApplyFunction(_F1ApplyFunction(x),x)=_c[1] _F1

  ApplyFunction(x),diffApplyFunction(diffApplyFunction(_F2

                                                    \
                                                    |
  ApplyFunction(y),y),y)=_c[1] _F2ApplyFunction(y)}]|
                                                    /

No solution appears when the differential equation is expressed in standard form, but when exp(x + y) is converted to

exp(1)^(x + y) the correct solution appears.

 

Can anyone help with forcing this to simplify

assume(x>0)

assum(y>0)

simplify(sqrt(-x^2-y^2))

I am looking for this to force the sqrt to return as the imaginary number multiplied by the square root of x^2+y^2

simplify(sqrt(-x^2)) does simplify as far as bringing in the imaginary number 

Many thanks

Hello
I solved an equation using Maple . but in answer there is RootOf statement that I can't change to a simple statement without RootOf.

restart

``

``

((Lr2*(vo+vs)*sqrt(Lr1*Lr2)+vo*Lr1*sqrt(Lr1*Lr2))*sin(t*sqrt((Lr1+Lr2)/(Lr1*Lr2*cr)))*sqrt(cr*(Lr1+Lr2))+vs*t*Lr1*(Lr1+Lr2))/((Lr1+Lr2)^2*Lr1)

((Lr2*(vo+vs)*(Lr1*Lr2)^(1/2)+vo*Lr1*(Lr1*Lr2)^(1/2))*sin(t*((Lr1+Lr2)/(Lr1*Lr2*cr))^(1/2))*(cr*(Lr1+Lr2))^(1/2)+vs*t*Lr1*(Lr1+Lr2))/((Lr1+Lr2)^2*Lr1)``

(1)

eq := ((Lr2*(vo+vs)*sqrt(Lr1*Lr2)+vo*Lr1*sqrt(Lr1*Lr2))*sin(t*sqrt((Lr1+Lr2)/(Lr1*Lr2*cr)))*sqrt(cr*(Lr1+Lr2))+vs*t*Lr1*(Lr1+Lr2))/((Lr1+Lr2)^2*Lr1)

((Lr2*(vo+vs)*(Lr1*Lr2)^(1/2)+vo*Lr1*(Lr1*Lr2)^(1/2))*sin(t*((Lr1+Lr2)/(Lr1*Lr2*cr))^(1/2))*(cr*(Lr1+Lr2))^(1/2)+vs*t*Lr1*(Lr1+Lr2))/((Lr1+Lr2)^2*Lr1)

(2)

solve(eq, t)

-(Lr1*Lr2)^(1/2)*(Lr1*cr+Lr2*cr)^(1/2)*sin(RootOf(Lr1*sin(_Z)*(Lr1*cr+Lr2*cr)^(1/2)*((Lr1+Lr2)/(Lr1*Lr2*cr))^(1/2)*(Lr1*Lr2)^(1/2)*vo+Lr2*sin(_Z)*(Lr1*cr+Lr2*cr)^(1/2)*((Lr1+Lr2)/(Lr1*Lr2*cr))^(1/2)*(Lr1*Lr2)^(1/2)*vo+Lr2*sin(_Z)*(Lr1*cr+Lr2*cr)^(1/2)*((Lr1+Lr2)/(Lr1*Lr2*cr))^(1/2)*(Lr1*Lr2)^(1/2)*vs+_Z*Lr1^2*vs+_Z*Lr1*vs*Lr2))*(Lr1*vo+Lr2*vo+Lr2*vs)/(Lr1*(Lr1+Lr2)*vs)

(3)

``

Download spr.mw

How can I simplify to an answer without RootOf?

Thank u

I want to create a 2D and 3D graph of the following question. Evaluate F xy+y+z along the curve r(t)=2ti+tj+(2-2t)k, 0<=t<=1 I found the line integral to be 13/2. I am just stuck on how to graph this in 2D and 3D.

Thank you all in advance! I enjoy learning all the new tricks in Maple from you all.

Hello

I am not familiar with the use of notsero in SolveTools:-PolynomialSystem. Is there any special syntax to use it?  In the following example, the trivial solution {x=0,y=0} is to be eliminated.  

SolveTools:-PolynomialSystem({x*(x^2 - 2), y*(y^2 - 2)}, {x, y},explicit=true)

If I issue the command

SolveTools:-PolynomialSystem({x*(x^2 - 2), y*(y^2 - 2)}, {x, y},{x,y},explicit=true)

all roots with either x=0 or y=0 are eliminated.  

Can netzero be used to eliminate only the trivial solution?  

 

Many thanks

 

 

I'm trying to compute the numerical solution for a PDE using the numerical solution of a first-order ODE. I looked at the INTEGRATE keyword of the pdsolve function, but I'm not sure how to use it. Can someone show an example of how to use this keyword?

Hello,

I'm new at Maple, so I'm still trying to figure out basic stuff. I have solved an ode with t as independent variable and x as dependent one and I have used plots[odeplot] to plot x over t, but I also need to plot t over x. Any ideas how I can do that? Here's my code:

ode := diff(x(t), t) = 16250.25391*(1 - (487*x(t))/168 + 4*Pi*x(t)^(3/2) + (274229*x(t)^2)/72576 - (254*Pi*x(t)^(5/2))/21 + (119.6109573 - (856*ln(16*x(t)))/105)*x(t)^3 + (30295*Pi*x(t)^(7/2))/1728 + (7.617741607 - 23.53000000*ln(x(t)))*x(t)^4 + (535.2001594 - 102.446*ln(x(t)))*x(t)^(9/2) + (413.8828821 + 323.5521650*ln(x(t)))*x(t)^5 + (1533.899179 - 390.2690000*ln(x(t)))*x(t)^(11/2) + (2082.250556 + 423.6762500*ln(x(t)) + 33.2307*ln(x(t)^2))*x(t)^6)*x(t)^5

ics := x(0) = xlow

solx := dsolve({ics, ode}, numeric, range = 0 .. tfin)

plots[odeplot](solx, 0 .. tfin)

 

Hi

I have the following fractional  system of differential equation. How to plot it for alpha=0.5, beta=0.5?

eq1:=diff(y1(t),t$alpha)=0.04-(0.09*y1(t)*y2(t))-(0.00250*y1(t)*y2(t))/((0.03500+y2(t)))-0.04*y1(t);                                                                                                                                                                    

eq2:=diff(y2(t),t$beta)=(0.09*y1(t)*y2(t))+(0.00250*y1(t)*y2(t))/((0.035+y2(t)))-(0.02+0.04)*y2(t);

 

Hello

I have a funtion defined as 

a := diff(u*ln(m__o/(-q*t + m__o)) - g*t, t)

where m_0, q, g, and u are constants with dimensions. T is the variable and has dimensions as well. I need to print out columns of this function and other similar functions, v and h, in 4 seconds intervals of t. So what I have is this:

for i from -4 by 4 to 80 do
    if i = -4 then printf("%12s %18s %15s %15s \n", "time", "acceleration", "velocity", "altitude"); else printf("%10d %c %10.2f  %s %10.2f  %s %10.2f  %s \n", i, "s", eval(a, t = i), "ft/s^2", eval(v, t = i), "ft/s", eval(h, t = i), "mi"); end if;
end do

this works perfectly fine until I assign units to the constants and t. Then I get the error: Error, (in fprintf) number expected for floating point format. 

Then I also need to plot a v and h against t. Seems like plot doesn't work either with units.

 

So what do i do?

Thanks

Hello. I have the equations written into the arrays. I want to combine them into a common system and solve it. I gave a simple example of what I need. How do I perform this operation?

restart

T1 := array(1 .. 2);

array( 1 .. 2, [ ] )

 

x = 1

 

y = 2

(1)

T2 := array(1 .. 2);

array( 1 .. 2, [ ] )

 

z = 3

 

r = x+y+z

(2)

solve({T1, T2}, {r, x, y, z});

``


 

Download 4.mw

restart; with(Student[LinearAlgebra]); A := Matrix([[2, 3, -4], [0, -4, 2], [1, -1, 5]]); for i to 3 do for j to 3 do print((-1)^(i+j)*Minor(A, i, j)) end do end do; How to code to get that is egal to Adjoint(A)? Thank you.

Hi, 

Whenever I open Maple 2020 and type one single letter or number (doesn't matter) Maple 2020 will "freeze" and load forever (i have had it open for a long time, just watching that f**king blue circle spin...

I have tried reinstalling, repairing, running as admin, and changing the compatibility mode, still, nothing works:(

 

I run Maple 2020 as a Student with WithGym

Pc specs:

Intel i5-10300h 2.6 ghz

Geforce 1660 ti 6gb

Windows 10 x64

Hello there, 

Would you tell me how to check if the two expressions presented below are the same?

My simple attempt (at the end of the worksheet below) failed. 

This page might be helpful to check the equality: https://www.myphysicslab.com/springs/trig-identity-en.html
 

restart;

subexpx := Ls*cos(omega*t + phi__l + theta)*omega + sin(omega*t + phi__l + theta)*Rs;

Ls*cos(omega*t+phi__l+theta)*omega+sin(omega*t+phi__l+theta)*Rs

(1)

subexpx2 := sqrt((omega*Ls)^2+Rs^2)*sin(omega*t + phi__l + theta + arctan(omega*Ls/Rs));

(Ls^2*omega^2+Rs^2)^(1/2)*sin(omega*t+phi__l+theta+arctan(omega*Ls/Rs))

(2)

is(subexpx - subexpx2 = 0) assuming omega::positive, Ls::positive, Rs::positive;

false

(3)

 

 


Thank you,

Download Q20201108.mw

Hi
I want to say maple convert this radicals to a single radical expr.

cos(sqrt(Lr1+Lr2)*t/(sqrt(Cr)*sqrt(Lr1)*sqrt(Lr2)))

convert to :

cos(sqrt((Lr1+Lr2)/(Cr*Lr1*Lr2))*t)
thank u .

Hi,

 

I don't speak well in english but I 'll try

 

I can't print a matrix multiplication without maplke simplify it

i want 

A*b=x

so 

|1 2 3|     |x|        |1|

|4 5 6|  * |y|    =   |2|

|7 8 9|     |z|        |3|

but maple simplify A*x

so i have something like

|1x 2y 3z|            |1|

|4x 5y 6z|       =   |2|

|7x 8y 9z|            |3|

 

 

Thank a lot.

 

 

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