Items tagged with equation


     It is known that ODE boundary value problem is similar to the problem of solving systems of nonlinear equations. Equations are the boundary conditions, and the variables are the values of the initial data.
For example:

y '' = f (x, y, y '), 0 <= x <= 1,

y (0) = Y0, y (1) = Y1;

Where y (1) = Y1 is the equation, and Z0 is variable, (y '(0) = Z0).

     solve () and fsolve () are not directly suitable for such tasks. Directly should work the package of optimization in relation to a system of nonlinear equations. (Perhaps it has already been implemented in Maple.)
Personally, I am very small and unprofessional know Maple and cannot do it. Maybe there is someone who would be interested, and it will try to implement this approach to solving ODE boundary value problems?  

I have a system of equations e.g.


where A,B,C are Matrices and I want to solve for A.

Sure I can write every equations in brakets [..=0], but isn'T it possible to just use the matrix notation?


how i can solve two equation with respect to parameter sigma1

restart; pprime11 := -16395.36603*q1+5.811117425*q1*sigma1^2+3526.724044*p1-1.250000000*p1*sigma1^2+4.999870968*10^11*p1^3+4.999870970*10^11*p1*q1^2+7.967307034*10^14*p1^2*q1+4.999870966*10^12*sigma1*p1^2*q1-2.655769012*10^14*q1^3+4.999870968*10^12*sigma1*q1^3-17633.62022*q1*sigma1+6.250000000*q1*sigma1^3

qprime11 := 2.655769012*10^14*p1^3-7.967307034*10^14*p1*q1^2+4.999870970*10^11*p1^2*q1-4.999870968*10^12*sigma1*p1^3-4.999870966*10^12*p1*sigma1*q1^2+3526.724044*q1-1.250000000*q1*sigma1^2+16395.36603*p1-5.811117425*p1*sigma1^2+4.999870968*10^11*q1^3+17633.62022*p1*sigma1-6.250000000*p1*sigma1^3:

-50 < sigma1 and sigma1 < 50:

sigma1 <> 53.11665685, -53.11665685:

SOLL := solve({pprime11, qprime11}, real)

Warning,  computation interrupted







I am unable to use subs() command when using subscript : I'd like to replace YP__1 with dGx in the equation :

"Eq:= YP__1 = Y__2" (Eq:= YP1=Y2)


 so I have tried : subs({YP__1=dGx},Eq)


But it doesn't work... It give me : YP__1 = Y__2 and I would like to have dGx = Y__2


I have tried also with subs({YP[1]=dGx},Eq) but doesn't work too.


If I am not using subscript, for exemple : Eq:= YP1 = Y2


And do : subs({YP1=dGx},Eq)


That works great...


But I must use subscript __ because Eq is a result from ODEtools (convertsys).


Can you help me please ?


Thanks you very much.



When I was editing the head of the question (? instead of .), its body disappeared. Please, insert it again.


Markiyan Hirnyk

If L is a list [a,c,b,d,f,e]

S is a list [b,c,f,e]

I want to use the permutation opf S to rearrange L [b,c,f,e,a,d]

In my case a,b,c,d,e,f are equations.

I have checked many Maple pages and I found nowhere the answer to this question.

EQ:= s^2-4*s+1=3;

I need to print the following statement:

The Equation Is: EQ

I need the equation to appear where EQ is.

Thank you guys!

I appreciate it.




Here is a code

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/ .


A fragment of code

for b in extra_bcs do try print(b = 10^(-2)); res[b] := dsolve(dsys4 union {b = 10^(-2)}, numeric, initmesh = 2024, output = listprocedure, approxsoln = [omega2 = 0.1e-2, s(x) = cosh(upsilon*x)-cos(upsilon*x)-(cosh(upsilon)+cos(upsilon))*(sinh(upsilon*x)-sin(upsilon*x))/(sinh(upsilon)+sin(upsilon)), g(x) = sin(((2*n+1)*(1/2))*Pi)], abserr = 0.1e-1) catch: print(lasterror) end try end do; indx := indices(res, nolist); nops([indx]); res[indx[i]]; seq(subs(res[indx[i]](1), omega2(1)), i = 1 .. nops([indx]))


I would like to simplify a trigonometric equation that I obtain with a vectorial closure (in mechanics)

Here the equation that I would like to simplify 

eq_liaison :=(-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*l2[1]+((-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*cos(th(t))+(-cos(p(t)+g(t))*cos(a(t))+sin(a(t))*sin(b(t))*sin(p(t)+g(t)))*sin(th(t)))*l3[1] = 0

Do you have ideas so as to simplify again this expression ?

This expression can still be simplified. You can find here the result expected :

I find surprising that I have so many difficulties to make trigonometric simplications with the trigonometric functions.

Thank you for your help

PS : Sorry for duplicating posts. As I didn't receive any answer, I have tried to simplified my post to isolate the difficulty.

I am using maple 13 to get the resualt of the einstein filed equations




Estn := Einstein(metric, RICCI, RS);

displayGR(Einstein, Estn);


How can i put the resualt on a array element, so i can use it later on?




I would like to determine the position jacobian matrix from a set of constraint equations.

Here my constraint equations :


The jacobian matrix that I would like to determine is :


Can you help me to make a general procedure to calculate a jacobian position matrix from a set of constraint equations ?

Thank you for your help



I would like to simplify this following trigonometric expression :

eq_liaison:= x0(t)-sin(alpha0(t))*sin(gamma0(t))*sin(beta0(t))*xb[1]+sin(alpha0(t))*sin(beta0(t))*cos(gamma0(t))*zb[1]+sin(alpha0(t))*cos(beta0(t))*yb[1]+cos(alpha0(t))*sin(gamma0(t))*zb[1]+cos(alpha0(t))*cos(gamma0(t))*xb[1]+l2[1]*(sin(psi[1](t))*sin(alpha0(t))*sin(gamma0(t))*sin(beta0(t))-cos(psi[1](t))*sin(alpha0(t))*sin(beta0(t))*cos(gamma0(t))-sin(psi[1](t))*cos(alpha0(t))*cos(gamma0(t))-cos(psi[1](t))*cos(alpha0(t))*sin(gamma0(t)))+l3[1]*(sin(theta[1](t))*sin(psi[1](t))*sin(alpha0(t))*sin(beta0(t))*cos(gamma0(t))+sin(theta[1](t))*cos(psi[1](t))*sin(alpha0(t))*sin(gamma0(t))*sin(beta0(t))+cos(theta[1](t))*sin(psi[1](t))*sin(alpha0(t))*sin(gamma0(t))*sin(beta0(t))-cos(theta[1](t))*cos(psi[1](t))*sin(alpha0(t))*sin(beta0(t))*cos(gamma0(t))+sin(theta[1](t))*sin(psi[1](t))*cos(alpha0(t))*sin(gamma0(t))-sin(theta[1](t))*cos(psi[1](t))*cos(alpha0(t))*cos(gamma0(t))-cos(theta[1](t))*sin(psi[1](t))*cos(alpha0(t))*cos(gamma0(t))-cos(theta[1](t))*cos(psi[1](t))*cos(alpha0(t))*sin(gamma0(t)))-xp[1](t) = 0

I would like to make groups like : cos(a)cos(b) - sin(a)sin(b)=cos(a+b)  but keepind the maximum of expression products

On the following example (2 equations below), the function combine(expr,trig) works well 

eq_liaison[1] := cos(gamma(t))*r+(cos(gamma(t))*cos(psi(t))-sin(gamma(t))*sin(psi(t)))*l-x(t) = 0 
eq_liaison[2] := sin(gamma(t))*r+(sin(gamma(t))*cos(psi(t))+cos(gamma(t))*sin(psi(t)))*l = 0

But, I would like maple do only the first simplifications in order to the maximum of expression products. The function combine(expr,trig) goes too far in the first equation and I obtain only expression sums. 

Do you have ideas to simplify the first trigonometric equations
- with groups like : cos(a)cos(b) - sin(a)sin(b)=cos(a+b)
- and keeping products of expressions ?

Thank you for your help

A := Vector([1, 2, 3])

solve(2*A = 5+x, {x})


can anyone help me why i am having proble to solve for x?




For some reason my three equation with three unknowns won't be solved. Anyone who can help? I tried the following:

Really appreciate anyone who can help me out!


Hi, does anyone know how to choose the variables that populate the DAE Variables box when you use "equation extraction"?

I want the result to be in terms of the voltage source and the voltage drop across the capacitor for a RLC circuit.  I want to be able to choose the input-output variables for the final equation.



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