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Nm= p1. p2 ...pm + 1, for m more than or equals 1.

 

So N1 = p1 + 1 = 2 + 1 = 3, N2 = p1 p2 + 1 = 2  3 + 1 = 7, etc.

 

We prove that Nm is not divisible by any of p1, p2, . . . , pm, so that Nm is either a prime or it is divisible by a prime larger than pm.

 

(c) Use Maple to find out which of these numbers Nm, for m = 1, 2, . . . , 15, is actually prime.

 

Use Maple to compare pm with the smallest prime number that divides Nm, for m =1, 2, . . . , 15.

 

I want to simulate Inelastic collision

 

 

There has 2 ball which I can change  Quality and Radius.

 

 

 

one ball  move to another stirless ball with diferent angle

Hi all

I'm having a hard time, making Maple plot a pretty huge expression in my project.

I have solved a differential equation with initial conditions with method=laplace. The differential equation contains a fourier serie equation, so the more accurate i want the equation to be, the larger the differential equation will be.

Maple solves the equation just fine, and i can plot the solution with 2-4 fourier parts, but when i go higher as i need, the graph ends up empty?

with 20 parts i get the following equation: 

0.*sin(52.88*t)+0.*cos(74.03*t)-0.*sin(74.03*t)-0.*cos(52.88*t)+0.*cos(200.95*t)-0.*sin(200.95*t)+0.*cos(158.65*t)-5.55*10^(-8)*sin(105.76*t)-0.*sin(116.34*t)+0.*cos(31.73*t)-.45*sin(10.58*t)+1.02*cos(10.58*t)+0.*sin(95.19*t)+0.*cos(116.34*t)+0.*sin(179.80*t)-0.*cos(179.80*t)+0.*sin(137.49*t)-0.*sin(31.73*t)-0.*cos(95.19*t)+5.53*10^(-993)*(-1.13*10^992*cos(10.61*t)+8.14*10^991*sin(10.61*t))*exp(-0.7e-1*t)+4.23*10^(-7)*cos(211.53*t)-6.69*10^(-7)*cos(63.46*t)-6.11*10^(-7)*cos(105.76*t)+5.79*10^(-7)*cos(126.92*t)+6.67*10^(-8)*sin(42.31*t)-5.88*10^(-8)*sin(148.07*t)+5.88*10^(-8)*sin(211.53*t)+7.09*10^(-7)*cos(42.31*t)+5.45*10^(-8)*sin(84.61*t)+6.40*10^(-7)*cos(84.61*t)+5.72*10^(-8)*sin(126.92*t)-9.01*10^(-7)*cos(21.15*t)+5.97*10^(-8)*sin(169.22*t)+5.06*10^(-7)*cos(169.22*t)-5.98*10^(-8)*sin(190.38*t)-4.65*10^(-7)*cos(190.38*t)-5.44*10^(-7)*cos(148.07*t)-1.33*10^(-7)*sin(21.15*t)-5.61*10^(-8)*sin(63.46*t)-0.*cos(137.49*t)-0.*sin(158.65*t)

if i plot that expression, the graph ends up empty?

I did also try to solve the equation numerical to plot it with odeplot, but when i try to solve it without the laplace method i get this error message:
"Error, (in dsolve) found the following equations not depending on the unknows of the input system:"

The differential equation is:

ode:=diff(Theta(t), t, t)+2*Zeta*omega[balanceue]*(diff(Theta(t), t))+omega[balanceue]^2*Theta(t) = M[p]/m[balanceue]

and the initial conditions:

ICS := Theta(0) = (1/8)*Pi, (D(Theta))(0) = 0;

when i do:

dsolve({ICS, ode}, Theta(t), method = laplace) it solves just fine.

 

but when i try with:

dsolve({ICS, ode}, Theta(t))

or

dsolve({ICS, ode}, Theta(t),numeric)

I get the message: 

Error, (in dsolve) found the following equations not depending on the unknowns of the input system: {Theta(0) = (1/8)*Pi, (D(Theta))(0) = 0}

It doesnt seem logical at all, is it a bug? Or can anybody help me with this problem?


Regards

Nicolai

I have a three paramter ode problem that involves three tanks with given initial concentrations.  Overtime the concentration equalizes but one of the steps is to determine all bifurcation values.  Not sure how to continue with this number of variables.

 This is our given system with initial conditions

sys_ode := diff(x(t),t) = (-r*x(t))/100+0+(r*z(t))/50, 
> diff(y(t),t) = (r*x(t))/100+(-r*y(t))/25+0,
> diff(z(t),t) = 0+(r*y(t))/25+(-r*z(t))/50;
> x0:=0; y0 := 200; z0:=0;

limit evaluation...

November 20 2014 Aakanksha 20

> restart:
> m:=2; k:=1.0931; a:=k-m; b:=k+m-1;
m := 2
k := 1.0931
a := -0.9069
b := 2.0931
> z:=(k*m)/10^(0.1*10);
z := 0.2186200000
> simplify(((10^(0.1*yo))^((b-a+2*p-1)/2)*z^((b-a+2*p+1)/2)*GAMMA((1-(b-a+2*p))/2))/(p!*GAMMA(p-a+1)*GAMMA(1+((1-(b-a+2*p))/2))));
1 / 
---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654) exp(
GAMMA(p + 1.906900000) 

-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(
\
-1. - 1. p)/
> [seq(limit(.3183098861*sin(3.141592654*p+3.141592654)*exp(-3.040840432-1.520420216*p+.2302585095*yo)*(exp(.2302585095*yo))^p*GAMMA(-1.-1.*p)/GAMMA(p+1.906900000),p=k),k=0..10)]
Warning, inserted missing semicolon at end of statement, ...=k),k=0..10)];
[ / 1 / 
[limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654) 
[ \GAMMA(p + 1.906900000)


exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 / 
GAMMA(-1. - 1. p)/, p = 0|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \ 
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 1|, 
/

/ 1 / 
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654) 
\GAMMA(p + 1.906900000)


exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 / 
GAMMA(-1. - 1. p)/, p = 2|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \ 
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 3|, 
/

/ 1 / 
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654) 
\GAMMA(p + 1.906900000)


exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 / 
GAMMA(-1. - 1. p)/, p = 4|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \ 
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 5|, 
/

/ 1 / 
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654) 
\GAMMA(p + 1.906900000)


exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 / 
GAMMA(-1. - 1. p)/, p = 6|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \ 
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 7|, 
/

/ 1 / 
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654) 
\GAMMA(p + 1.906900000)


exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \ / 1 / 
GAMMA(-1. - 1. p)/, p = 8|, limit|---------------------- \0.3183098861 sin(
/ \GAMMA(p + 1.906900000)

3.141592654 p + 3.141592654) exp(-3.040840432 - 1.520420216 p

p \ \ 
+ 0.2302585095 yo) (exp(0.2302585095 yo)) GAMMA(-1. - 1. p)/, p = 9|, 
/

/ 1 / 
limit|---------------------- \0.3183098861 sin(3.141592654 p + 3.141592654) 
\GAMMA(p + 1.906900000)


exp(-3.040840432 - 1.520420216 p + 0.2302585095 yo) (exp(0.2302585095 yo))

\ \]
GAMMA(-1. - 1. p)/, p = 10|]
/]

 

 

 

 

 

why the solution is in limit approaches to form??? need to have a closed form expression. any help..????

test.mw

restart; with(LinearAlgebra)

``

dF := -.525*exp(-7*t)+2.625*exp(-3*t)+.8*exp(-4*t);

-.525*exp(-7*t)+2.625*exp(-3*t)+.8*exp(-4*t)

(1)

``

e3 := `<,>`(1, 1, 1); E := proc (m) options operator, arrow; IdentityMatrix(m) end proc; beta := `<|>`(.1, .6, .3); S := `<|>`(`<,>`(-3, 1, 1), `<,>`(1, -5, 2), `<,>`(0, 2, -4)); S0 := -S.e3

beta := Vector[row](3, {(1) = .1, (2) = .6, (3) = .3})

 

S := Matrix(3, 3, {(1, 1) = -3, (1, 2) = 1, (1, 3) = 0, (2, 1) = 1, (2, 2) = -5, (2, 3) = 2, (3, 1) = 1, (3, 2) = 2, (3, 3) = -4})

 

S0 := Vector(3, {(1) = 2, (2) = 2, (3) = 1})

(2)

Z := `<|>`(x, y, z)

Z := Vector[row](3, {(1) = x, (2) = y, (3) = z})

(3)

ME := MatrixExponential(S+Typesetting:-delayDotProduct(S0, Z), t);

`[Length of output exceeds limit of 1000000]`

(4)

MEint := map(int, ME.dF, t = 0 .. infinity)

Error, (in int) wrong number (or type) of arguments: wrong type of integrand passed to definite integration.

 

`&beta;plus&Assign;solve`(Z = beta.MEint, Z)

"(RTABLE(18446744074195006390,VECTOR([x, y, z]),Vector[row])=RTABLE(18446744074193876574,VECTOR([.1, .6, .3]),Vector[row]).MEint) betaplus:=solve (RTABLE(18446744074195006390,VECTOR([x, y, z]),Vector[row]))"

(5)

``

1step- I want to integrate the (ME*dF) from t=0 to ∞ .

2step- Evaluate Z=<x,y,z> by solving Z=β*MEint.

Download test.mw

hello, i went solve these equation ,with a & b take any value

b*x*ln(x)-x*ln(a)+a=0

thank you

I have a nonlinear system with 4 equations and 4 unknowns. I am using fsolve. I know that there are multiple solutions for each variable but am only getting one. I need the others. what do I do??

This is my code:

R__1 := Matrix([[1, 0] , [0, 1] ]);

R__2 := Matrix([[1/2, sqrt(3)/2] , [-sqrt(3)/2, 1/2] ]);

R__3 := Matrix([[-1/2, sqrt(3)/2] , [-sqrt(3)/2, -1/2] ]);

R__4 := Matrix([[-1, 0] , [0, -1] ]);

R__5 := Matrix([[-1/2, -sqrt(3)/2] , [sqrt(3)/2, -1/2] ]);

 

d__1 := Vector( [ 0, 5.4] );

d__2 := Vector( [ 6.4, 4.539] );

d__3 := Vector( [ 11, 4.078] );

d__4 := Vector( [ 15.5, 2.079] );

d__5 := Vector( [ 19, 1.039] );

 

a := Vector( [ a__x, a__y] );

 

A__1:=R__1.a+d__1;

A__2:=R__2.a+d__2;

A__3:=R__3.a+d__3;

A__4:=R__4.a+d__4;

A__5:=R__5.a+d__5;

 

OO:=Vector([O__x,O__y]);

 

DA1:=A__2.A__2-A__1.A__1-2*(A__2-A__1).OO;

DA2:=A__3.A__3-A__1.A__1-2*(A__3-A__1).OO;

DA3:=A__4.A__4-A__1.A__1-2*(A__4-A__1).OO;

DA4:=A__5.A__5-A__1.A__1-2*(A__5-A__1).OO;

 

fsolve({DA1,DA2,DA3,DA4},{a__x,a__y,O__x,O__y});

Thanks for any tips you may be able to offer

 

Hey, how is can i see all the steps in maple? I would specially like to know it for differential equations.

For example we could use this one:

dl := 3*(diff(y(t), t, t))+6*(diff(y(t), t))+4*y(t) = 0 

hello, I have a list of numbers, for example [1.2,5.6,7.2,0.5,-0.25,-4,6]. I would like to find the position of it in the list where the number is closest to zero. May I know if there is a function for this please? Thanks.


restart:

m:=2; k:=10.1; a:=k-m; b:=k+m-1;

m := 2

k := 10.1

a := 8.1

b := 11.1

z:=(k*m)/10^(0.1*15);

z := .6387800873

yo:=10^(0.1*10);

yo := 10.

N1:=evalf(sum(((((yo/z)^((b-a+2*p-1)/2))*GAMMA((1-(b-a+2*p))/2))/(p!*GAMMA(p-a+1)*GAMMA(1+((1-(b-a+2*p))/2)))),p=0..10));

Error, (in NumericRange) summand is singular in the interval of summation

N2:=evalf(sum(((((yo/z)^((b+a+2*p-1)/2))*GAMMA((1-(b+a+2*p))/2))/(p!*GAMMA(p+a+1)*GAMMA(1+((1-(b+a+2*p))/2)))),p=0..10));

N2 := -701860.9759

 

 

 

 

 

 

 


Download mmgf_part1.mw

 

Any help???

Hi every body:

i will earn the cofficients of q(T),q(T)^2 and (diff(q(T), T, T)) with commonds maple,how?


eq := 324.6463527*(diff(q(T), T, T))+4.012505275*10^11*q(T)+3.589858529*10^12*q(T)^2 = 0;

i am solving 3 ODE with boundary condition.. with boundary condition

 

b.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/b.mw .

Download b.mw

 

then i got this error

Error, (in dsolve/numeric/bvp) initial Newton iteration is not converging

i dont know where i need to change.. could you help me..

 

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