Hi,

I have a second order differential equation

d2y/dt2 = -6.478831125*sin(y)

to be solved numerically. I've successfully been able to solve it using the 4th order Runge-Kutta method, however it is not properly written as a procedure and I'm unsure of how to do this.

So far I have:

R:= -6.478831125
z[0]:= 0:
y[0]:= Pi/2:
h:= 0.01:
t:= 10:
for i from 0 to t-1 by 1 do
c0:= evalf(h*R*sin(y[i])):
k0:= evalf(h*(z[i])):

For the equation x'(t)=F(z), z=(x,y), with the vector field

F(x,y)= [- x(x^4 + y^4) - y,  x  - y(x^4+y^4)]

prove that the origin is an attractor in the future, i.e., every solution verifies:

limit as t goes to +infinity of z(t) = 0

I need to format my answer as a regular mathematical proof.

Any ideas?

Hello guys ,

i have a complicated function , i found its roots but when i evaluate function by its roots , the result is not zero !!!

thank you for your helpWork.mw

An attendant at the zoo has a bag of peanuts to feed the monkeys. If the nuts are shared equally among the

7  monkeys in the first room, or among the 11 monkeys in the second room, there will be 3 nuts left over. If the nuts are shared equally among the 13 monkeys in the third room, there will be 10 nuts left over. but if the nuts are shared equally among all the monkeys in all the three rooms, there will be none left over. how many peanuts does the the attendant have?

It's interesting that every continuous piecewise linear function can be specified by one explicit equation with absolute values​​. The procedure JoggedLine carries out such conversion.

Formal arguments of the procedure: 

A - a list of the coordinates of the vertices of the polyline or the continuous piecewise linear expression defined on the entire real axis.

B (optional) - a point on the left "tail"...

Hi,

I'm trying to make a phase plane plot for the Lorenz system of differential equations around the equilibrium point (0,0,0) but when it keeps coming up with an error, saying it's "unable to obtain field plot, additional unknown(s) found: xy"

Any idea where I'm going wrong? Any help would be greatly appreciated!

Katie

sys1 := [diff(y(x), x) = a/(1-y(x))^b+c*exp(-d*x)/(1-y(x))^2]:

dsolve(sys1)

but the result is empty.

What can I do?

Hi all,

Is there any way to fill in colour to a polar plot using Maple 16? What I want to do is essentially make a coloured in pie slice using a defined radius and theta range.

I am aware of the function filled, which adds colour starting from the x-axis but that is not appropriate in this situation. I know of the filledregions function but that only works for implicit and contourplot, and as of yet I have not been able to use implicit...

Which command is similar with IsNull function in VBA for assign 0 when detect not assigned

I want to find shortest time it takes particle to travel from point A(0,0) to B(1,1). I tried to solve this problem by using following code test.mw. I know that solution to this problem is cycloid and i already found its equations in parametric form.

My problem is that when i try to solve integral as a solution i receive Time := Float(infinity)*I.

Is there any way to get a numeric solution in Maple...

Are There  options to solve this problem?

I solved a PDE system and got module() export plot,plot3d,animate,value,settings; ... end module (Got ui(x,t) and ur(x,t))
And after it I try to solve the task
Xs := [0, .175, .789, 1.818, 3.287, 5.183];
n := 1;
interface(prettyprint = 1);
for t1 from 0 by 50 to 50 do
k1 := sol:-value(t1, output = listprocedure);

(b0*z^n+b1*z^(n-1) + ... + bn) / (a0*z^n+a1*z^(n-1)+... + a_n_minus_m*z^m)

expand
into

beta0 + beta1*(1/z) + ... + betam*(1/z^m) + beta_m_plus_1*r_m_plus_1(z)/a(z) + ... + betan*rn(z)/a(z)

> de := (1/4)*U*(diff(S(y)^4, `$`(y, 2))) = C*P1*((O*exp(G*y)-R*exp(J*y))/(P1*(exp(J*L)-exp(G*L)))+P2/P1);

print(`output redirected...`); # input placeholder
/ 2 \
1 | 2 / d \ 3 / d / d \\| /
- U |12 S(y) |--- S(y)| + 4 S(y) |--- |--- S(y)||| = C P1 |
4 \ \ dy / \ dy \ dy /// \

O exp(G y) - R exp(J y) P2\
------------------------ + --|

Help me please, How to get a spatial derivative?After solving a system of differential equations numerically, I got module.Help please, How can I find a  value of the first derivative? 
For example , after solving the PDE system, module() export plot,plot3d,animate,value,settings; ... end module
 So, I need to find diff(U(x,t),x) (for example x=0 and t=0) 

Hi,

Here an example of integral that Maple 17 cannot calculate (mean of standard Gumbel distribution)

> G:=int(x*exp(-x)*exp(-exp(-x)), x = -infinity .. infinity);

The result is known as the Euler-Mascheroni constant as shown by a numerical computation:

 > evalf(G);

0.5772156649

>  identify(%, extension = [gamma]);

gamma

> evalf(gamma)

0.5772156649

Also, it cannot compute the variance