I have system of equation contain of two equations

eq1:=a1*x^2+b1*y^2+c1*x*y+d1*x+e1*y+f1:
eq2:=a2*x^2+b2*y^2+c2*x*y+d2*x+e2*y+f2: 

I want to find the number k so that the equation

a1*x^2+b1*y^2+c1*x*y+d1*x+e1*y+f1 + k*(a2*x^2+b2*y^2+c2*x*y+d2*x+e2*y+f2) = 0

can be factor, where k satisfy

a:=a1+k*a2:
b:=b1+k*b2:
c:=c1+k*c2:
d:=d1+k*d2:
e:=e1+k*e2:
f:=f1+k*f2:

I tried

A:=a*x^2+b*y^2+c*x*y+d*x+e*y+f:
collect(A,x);
B:=collect(discrim(A, x), y);
C:= discrim(B,y);

and got the expression

-16*(4*a*b*f-a*e^2-b*d^2-c^2*f+c*d*e)*a=0.

For example 

> restart:

a1:=14:

b1:=-21:

c1:=0:

d1:=-6:

e1:=45:

f1:=-14:

a2:=35:

b2:=28:

c2:=0:

d2:=41:

e2:=-122:

f2:=56:

a:=a1+k*a2:

b:=b1+k*b2:

c:=c1+k*c2:

d:=d1+k*d2:

e:=e1+k*e2:

f:=f1+k*f2:

P:=c*d*e+4*a*b*f-a*e^2-b*d^2

-f*c^2:

eq1:=a1*x^2+b1*y^2+c1*x*y+d1*x+e1*y+f1:

eq2:=a2*x^2+b2*y^2+c2*x*y+d2*x+e2*y+f2:

with(RealDomain):

Q:=solve(P=0,k);

factor(eq1+Q*(eq2));

solve([

eq1=0,eq2],[x,y]);

Where, Q is k which I want to find. 

My question is, if I have the system of equations

eq1:=a1*x^3+b1*y^3+c1*x^2*y+ d1*x*y^2 + e1*x+f1*y+g1:
eq2:=a2*x^3+b2*y^3+c2*x^2*y+ d2*x*y^2 + e2*x+f2*y+g2: 

How can I get a similar to the 

-16*(4*a*b*f-a*e^2-b*d^2-c^2*f+c*d*e)*a=0?

In that attached file is a multip step problem that involves graphing a right circular cylinder using transtion matrices and orthonormal basis. I have completed the hole question minus the very last part which is asking for new parametric equations for the cylinder if its center point is located at (-2, 10, 3) instead of the origin.

Any ideas on how to do this will be greatly appreciated.

question_4.mw

the sequence is non-decreasing up to some point after which it is non-increasing. Note that i can be 1 or n. A constant sequence is considered to be unimodal.

Examples of unimodal lists:

[1, 1, 1, 1, 1],
[1, 2, 2, 3, 4, 5, 5, 5],
[5, 5, 4, 4, 3, 3, 1],
[1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1],
[1, 2, 2, 3, 3, 3, 4, 4, 2, 2, 1, 1, 1]

Examples of lists that are not unimodal:

[1, 0, 1, 0],
[1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1],
[1, 1, 2, 2, 3, 4, 5, 2, 2, 6, 4, 2, 2, 1, 0]

i don't have a clue

I am trying to make a substitution:

> restart;
> f1 := conjugate(z)^2*z^2;
> f2 := applyrule(z*conjugate(z) = x, f1);

however the result is

f2 := conjugate(z)^2*z^2

Do you have any ideas how to solve the problem? Thank you.

Hi,

I have a finite difference method used to solve my problem.  My unknown function u(x,y,t) is found using the finite difference method, i would like to plot the solution for different time, and I can do this...

Only I want to make an animation in time if it's possible, and someone can help me.

Sol_animation.mw

Thnaks for helping me.

Hi, 

I love programming in Maple and I am interested in using MapleNet to display Maplets I have created. However, I am a novice in software and web technology. My questions, do I only need creating Maple worksheets, establishing interfaces and uploading the worksheets at an appropriate server in order to be able using MapleNet without any additional software? Can MapleNet display both GUI-based and command-driven-based Maplets on the web? Btw, I already read and downloaded "5 Developing Worksheets for MapleNet" but I do not fully understand its contents due to technical terms used in it.

I noticed that the following website: http://www.maplenet.net/ offers web services commercially. Does this website
have any relationship with MapleNet from Maplesoft or one of the most appropriate servers to upload and play our worksheets with MapleNet?

Thanks in advance for any helpful reply.

Loeky

email: L.Haryanto@unhas.ac.id

Hi:

how i can dimensionless a equation in maple?is there direct method for dimensionless equation in maple?for example i must dimensionless the below equation:

c1*f(x, t)+c2*(diff(phi(x, t), x))+c3*(diff(w(x, t), x, x))+c4*(diff(w(x, t), t, t)) = 0

dimensionless values are defined as:

X=x/l , T=(k/h)*t

where:

c1,c2,c3,c4 are constant cofficients.

my new equation must in terms of: X and T.

Hi, I have a homework to do that I am strugling with:

write a procedure which uses euler's method to solve a given initial value problem.
the imput should be the differential equation and the initial value.
using this programme find y(1) if dy/dx= x^2*y^3 and y(0)=1, and use maple dsolve command to check the solution.

That is what I have managed to do, but somehow it is not working correctelly, can somebody help please?

eul:=proc(f,h,x0,y0,xn)
  local no_points,x_old,x_new,y_old,y_new,i:
  no_points:=round(evalf((xn-x0)/h)):
  x_old:=x0:
  y_old:=y0:
 
  for i from 1 to no_points do
      x_new:=x_old+h:
      y_new:=y_old+evalf(h*f(x_old,y_old)):
      x_old:=x_new:
      y_old:=y_new:
  od:
  y_new:
end:


Thanks

Hi all.

Assume that we have partitioned [0,a], into N equidistant subintervals and in each subinterval we have M sets of poly nomials of the following form:

where T_m(t)=t^m( namely Taylor Series) and t_f is a(final point)
for Example with N=4, M=3 we have:

now we want to approximate a function, asy f(t), in this interval with following form:

How can we do this with maple????

how can we find the c_i's?????

Thanks a lot

Mahmood   Dadkhah

Ph.D Candidate

Applied Mathematics Department

assuming a equations likes this:

tan(x)+y*sin(x)=1;

tan(x)-y*sin(x)=0;

I want to solve this equations using LinearSolve function(do not use solve()). I  fisrtly change tan(x)=u,y*sin(x)=v and then solve u,v using LinearSolve. finally, I obtain x=atan(u), y=v/sin(x).

the question is how can I perform the above operates neatly? I know I can achive this by using a lot of subs().but is there any tools in maple do this neatly just like IntegrationTools[Change]?

Hai everyone. I used maple 12 and have an equation as follow:

int(int(lambda[v]*lambda[t]*exp(-lambda[v]*v-lambda[t]*t), v = (1/2)*(q[p]+q[p]*t[c]*t+2*S[di]*h*t)/(h*t) .. infinity), t = 0 .. infinity)

and try to get an outcome as follow:

However, I cannot get the outcome like I want. The maple just diplay the equation. Any tips or suggestion?

Thanks

Regards,

Dolby87

I say 

A:=1

R:=8.3

T=298

And do A/RT and I get a number answer. Sucess!.

Then I close the program. Open it again. Type A/RT and it spits out A/RT.

How do I get to not forget what the numbers were? 

question_4.pdf

I am reciving an error code when trying to graph the right circular cylinder in the questions

Attached is what I have done with the question.

Any help will be greatly appreciated. 

I have numerically solved a system of ODEs and plotted the graphs of a[j](t) for each j=0..21.

It was clear from the picture that each a[j] has a unique zero. Is there a maple command to

locate these zeroes?

I often use RegularChains and SolveTools package. SemiAlgebraic is extremelly useful to deal with polynomial equations. However, I need some similar to Mathematica's Resolve that allows me to eliminate some variables from the description of the set. Say we have some set decribed by: for all 0<x<1, p(x,z)> 0 where p is a polynomial in x and z. Is there any Maple command that allow us to remove x and give the set only n terms of z?