Items tagged with solve

Part of my research involves finding solutions to polynomial equations in several variables. Presently, I'm using Maple to both generate and solve these systems. With what I'll call a particular type of system the solve function returns several solutions, one of which has a particular variable free and the others where this variable is the root of a polynomial. By finding the roots of the polynomial, I can see that these solutions simply correspond to the solutions where the parameter is free.

So I'm trying to understand why this happens. Using the option dropmultiplicity=true has no effect, and there are no other details that I could find in the documentation. This question is ill-posed, I know, but any help would be appreciated.

hi...why solve for this equation dos not answer?

thanks

4.mw
 

restart; dsys3 := {diff(w(x), x, x, x, x, x, x)+diff(w(x), x, x, x, x)+diff(w(x), x, x)+(1-2)*w(x) = -90, w(0) = 0, w(1) = 0, ((D@@1)(w))(0) = 0, ((D@@1)(w))(1) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(1) = 0}; dsol5 := dsolve(dsys3, numeric, abserr = .1, output = array([.5]))

array( 1 .. 2, 1 .. 1, [( 1, 1 ) = (array( 1 .. 7, [( 1 ) = (x), ( 2 ) = (w(x)), ( 3 ) = (diff(w(x), x)), ( 4 ) = (diff(diff(w(x), x), x)), ( 5 ) = (diff(diff(diff(w(x), x), x), x)), ( 6 ) = (diff(diff(diff(diff(w(x), x), x), x), x)), ( 7 ) = (diff(diff(diff(diff(diff(w(x), x), x), x), x), x))  ] )), ( 2, 1 ) = (array( 1 .. 1, 1 .. 7, [( 1, 7 ) = (HFloat(-1.3899459757465982e-7)), ( 1, 3 ) = (HFloat(4.5022670883498417e-8)), ( 1, 1 ) = (.5), ( 1, 6 ) = (HFloat(2.2858770405958895)), ( 1, 5 ) = (HFloat(2.6615438731474126e-8)), ( 1, 4 ) = (HFloat(-0.04747952956114616)), ( 1, 2 ) = (HFloat(0.0019672907400671725))  ] ))  ] )

(1)

"restart;w(x):=C1* (sinh(x))+C2* (cosh(x))+C3 *(sin(x))+C4 *(cos(x))+C5 *(sin(x))+C6 *(cos(x))+90"

proc (x) options operator, arrow; C1*sinh(x)+C2*cosh(x)+C3*sin(x)+C4*cos(x)+C5*sin(x)+C6*cos(x)+90 end proc

(2)

A1 := evalf(subs(x = 0, w(x)))

90.+1.*C2+1.*C4+1.*C6

(3)

A2 := evalf(subs(x = 1, w(x)))

1.175201194*C1+1.543080635*C2+.8414709848*C3+.5403023059*C4+.8414709848*C5+.5403023059*C6+90.

(4)

A3 := evalf(subs(x = 0, diff(w(x), x)))

1.*C1+1.*C3+1.*C5

(5)

A4 := evalf(subs(x = 1, diff(w(x), x)))

1.543080635*C1+1.175201194*C2+.5403023059*C3-.8414709848*C4+.5403023059*C5-.8414709848*C6

(6)

A5 := evalf(subs(x = 0, diff(w(x), x, x, x)))

1.*C1-1.*C3-1.*C5

(7)

A6 := evalf(subs(x = 1, diff(w(x), x, x, x)))

1.543080635*C1+1.175201194*C2-.5403023059*C3+.8414709848*C4-.5403023059*C5+.8414709848*C6

(8)

solve({A1, A2, A3, A4, A5, A6}, {C1, C2, C3, C4, C5, C6})

``

solve*{A5, A6, C1, C2, C3, C4, C5, C6, 1.*C2+1.*C4+1.*C6, 1.*C2*upsilon^2-1.*C4*kappa^2-1.*C6*varsigma^2, C1*sinh(upsilon)+C2*cosh(upsilon)+C3*sin(kappa)+C4*cos(kappa)+C5*sin(varsigma)+C6*cos(varsigma), C1*upsilon^2*sinh(upsilon)+C2*upsilon^2*cosh(upsilon)-1.*C3*kappa^2*sin(kappa)-1.*C4*kappa^2*cos(kappa)-1.*C5*varsigma^2*sin(varsigma)-1.*C6*varsigma^2*cos(varsigma)}

(9)

``

``

``


 

Download 4.mw

 

Up to http://www.maplesoft.com/support/help/Maple/view.aspx?path=solve&term=solve

• 

If the solve command does not find any solutions, then if the second argument is a name or set of names, then the empty sequence (NULL) is returned; if the second argument is a list, then the empty list is returned. This means that there are no solutions, or the solve command cannot find the solutions. In the second case, a warning is issued, and the global variable_SolutionsMayBeLost is set to true.

 Let us consider 

solve({x > -Pi, (tan(x)-tan(x)^2)^2-cos(x+4*tan(x)) = -1, x < Pi}, [x]);
                               []

We see the command omits the solution x=0 without any warning. It should be noticed that Mathematica solves it, outputting

{{x -> 0}, {x -> 0}}

and the warning

Solve::incs: Warning: Solve was unable to prove that the solution set found is complete.

One may draw a conclusion on her/his own.

 

Hi,

I want to solve 2 linear equations in p[1] and p[2] 

eq3 = -(1/8)*(x^2+y^2+((x^2+y^2)^2+2*(omega[1]-omega[2])*(x^2-y^2)+(omega[1]-omega[2])^2)^(1/2)+omega[1]-omega[2])*(x^2*p[1]+2*x*y*p[2]-y^2*p[1]-((x^2+y^2)^2+2*(omega[1]-omega[2])*(x^2-y^2)+(omega[1]-omega[2])^2)^(1/2)*p[1]+omega[1]*p[1]-omega[2]*p[1])/(y^2*x*(omega[1]-omega[2])) - P[1];
eq4 = -(1/8)*(x^2*p[1]+2*x*y*p[2]-y^2*p[1]+((x^2+y^2)^2+2*(omega[1]-omega[2])*(x^2-y^2)+(omega[1]-omega[2])^2)^(1/2)*p[1]+omega[1]*p[1]-omega[2]*p[1])*(x^2+y^2-((x^2+y^2)^2+2*(omega[1]-omega[2])*(x^2-y^2)+(omega[1]-omega[2])^2)^(1/2)+omega[1]-omega[2])/(y^2*(omega[1]-omega[2])*x) - P[2]

solve({eq3,eq4},{p[1],p[2]});

I don't receive any answer. Why?

 

hi there,

this is my first post here, and first time using maple

I do have trigonometric system of equations, and I like to solve for thetas(1-5).

please help me out( how do I inpu them in maple) and how to solve them? 

how to configure maple to show every steps it run when solve a equation or system?

if so,

can i run the steps again and return the same result as a solve function do?

Am trying to valid a research work done by kuiken(1968)

Kuiken_(1968).pdf

where we have this two eauations:

restart;
Digits := 35;
with(ODETools);
with(student);
with(plots);
inf := 4;
equ1 := diff(f[0](eta), `$`(eta, 3))+theta[0](eta);
equ2 := diff(theta[0](eta), `$`(eta, 2))+3*f[0](eta)*(diff(theta[0](eta), eta));
Bcs1 := f[0](0) = 0, (D(f[0]))(0) = 0, theta[0](0) = 1, theta[0](inf) = 0, (D(D(f[0])))(inf) = 0;
S1 := dsolve({Bcs1, equ1, equ2}, {f[0](eta), theta[0](eta)}, type = numeric, method = bvp[midrich]);
proc(x_bvp)  ...  end;
S1(0);
[                            d                   
[eta = 0., f[0](eta) = 0., ----- f[0](eta) = 0., 
[                           deta                 

    d   /  d            \                                          
  ----- |----- f[0](eta)| = 0.82449782146165697398999365896678734, 
   deta \ deta          /                                          

  theta[0](eta) = 1.0000000000000000000000000000000000, 

    d                                                         ]
  ----- theta[0](eta) = -0.71098574970825563256340736114251047]
   deta                                                       ]
S1(inf);
[                                                            
[eta = 4., f[0](eta) = 1.7815670728545914261072119522795076, 
[                                                            

    d                                                      
  ----- f[0](eta) = 0.51061876174095320088291844433043562, 
   deta                                                    

    d   /  d            \                           
  ----- |----- f[0](eta)| = 0., theta[0](eta) = 0., 
   deta \ deta          /                           

    d                                                             
  ----- theta[0](eta) = -0.000054818176138173095945902421930470836
   deta                                                           

  ]
  ]
  ]
 

 

Pls, I need to find the function of the limit of f[0](eta) at eta tend to infinity. checked equation 45 of the attached document and for the two equation pls checked equation 36 and 37 for the ODE equation solved above.

Kuiken_solution for equation 36 and 37.pdf

Pressure_loss.mw

Hey all, could someone pls help me with how i can setup the equation for f in my worksheet. It should look like v and Rey with 45 data points. I've tried alot but i can't seem to solve it mysefl. Is it because i solve and map at the same time?

Thanks

ha := (diff(c(t), t))/(c(t)*(diff(c(t), t))-c(t));
solve(subs(m=ha,f(m))*subs(m=subs(c(t)=a(t),ha)), f(m)) = subs(m=ha+subs(c(t)=a(t),ha), f(m), f);

just expect to find a function ?
 

I have in mind all the real roots of the equation 2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0.

Maple fails with it:

>RealDomain:-solve(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0, t);

RootOf(tan(_Z)*tan(_Z^2/Pi)^2-tan(_Z)+2*tan(_Z^2/Pi))/Pi

 Even its numerical solution has gaps.

>Digits := 15; a := Student[Calculus1]:-Roots(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0, t = -2 .. 2);
Warning, some roots are returned as numeric approximations
 [-1.35078105935821, -1.18614066163451, -1.00000000000000, 0, 

   1.00000000000000, 1.28077640640442, 1.68614066163451,    1.85078105935821]

>nops(a);

8

>b := Student[Calculus1]:-Roots(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0, t = -2 .. 2, numeric);
 [-1.35078105935821, -1.18614066163451, -1.00000000000000, 

   -0.780776406404415, 0., 1.00000000000000, 1.28077640640442, 

   1.68614066163451, 1.85078105935821, 2.00000000000000]
>nops(b);
                               10


whereas 

>plot(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2, t = -2 .. 2);

shows 14 solutions.

The output of the command

>identify(a);

[1/4-(1/4)*sqrt(41), 1/4-(1/4)*sqrt(33), -1, 0, 1, 1/4+(1/4)*sqrt(17), 1/4+(1/4)*sqrt(33), 1/4+(1/4)*sqrt(41)]

suggests a closed-form expression for the roots.

Hello,

I'm a quiet perplexed  in front of the result of the function solve for trigonometric equations.

The result of this equation solve(cos(x)=a,x); is arccos(a) and the solution -arcos(a) is not given.

In order to have the other solution (-arccos(a)), I try this solve({cos(x)=a,x>Pi/2,x<3*(Pi/2)},x); but without success.

1) How can I obtain all the solution with the solve function with trigonometric equation and only symbolic equations (no numerical value)?

2) Is it possible to obtain a specific solution by defining the definition domain of the variables in the equation ?

Thanks a lot for your help

I have tried to solve the following ode equation, but I have got error. What is the potencial problem?

http://i65.tinypic.com/xdcl8p.jpg

 

 error

 

Hello,

I have to solve numerical trogonometric equations such as :
solve(.3707752782+.1499320455*sin(theta[4](t))+.1117559025*cos(theta[4](t))=0.5,theta[4](t));

But, after, I would like to keep only the solution defined in a specific interval such as : [0,Pi]

1) Is there a possibility to define options with the function solve to limit the solutions belonging to a specific interval ?

2) Otherwise, may you help me to make an systematic process to choose a solution in a specific interval ?

Thank you for your help

 

I mean the root of the equation

GAMMA(n-1/n)*GAMMA(1/n)/(n*GAMMA(n)) = 1

belonging to RealRange(Open(1),4). It should be noticed there are solutions outside this interval. Here is my try.

 

``

solve({n > 1, GAMMA(n-1/n)*GAMMA(1/n)/(n*GAMMA(n)) = 1, n < 4}, [n])``

[]

(1)

`in`(which*is*wrong, view*of)

simplify(eval(GAMMA(n-1/n)*GAMMA(1/n)/(n*GAMMA(n)), n = (1/2)*sqrt(5)+1/2))

1

(2)

Also

Student[Calculus1]:-Roots(A = 1, n = 1 .. 4)

[1.618033989]

(3)

There is a substitute

fsolve(GAMMA(n-1/n)*GAMMA(1/n)/(n*GAMMA(n)) = 1, n = 1 .. 4)

1.618033989

(4)

NULL

identify(%)

(1/2)*5^(1/2)+1/2

(5)

``

There is a shade of hope that GAMMA(n-1/n)*GAMMA(1/n)/(n*GAMMA(n))  can be simplified.

Download solution.mw

 PS. An SCR was submitted by me.

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