Use the Maple command DEplot to draw a direction field for the equation

make sure it at least covers the area −1 ≤ x ≤ 1,
−1 ≤ y ≤ 1

the equation is dy/dx+4y^3 −3y = 0.

then I have :

y(x):=dy/(dx)+4*y^(3)-3*y=0

with(DEtools); DEplot(y(x), x = -1 .. .1, y = -1 .. .1);

Error, (in DEtools/DEplot) vars must be declared as a list, e.g. [x(t),y(t),...]

so how can I change the command to make it work..

Its a well known fact that the spherical harmonics are eigenfunctions of the Laplace operator on the unit sphere with eigenvalues -l(l+1). Its used all over the place in QM for example. However maple does not seem to have this. 

Try it, you might be surprised. Its going to be a mess. How do you deal with it, to simplify it to the known form -l(l+1)r^-2Y_lm??

1.   can not  define  equation  when not known  E

Hello friends,

I want to derive the function of a curve. It's easy in for example "xyExtract" but I don't know how to do it in maple. please help. thank you all.

Hi

I need sort data of an imported matrix to ordered pairs.

'M' is a matrix with 2 columns and unknown numbers of row.

with(LinearAlgebra):

M := RandomMatrix(12, 2);

pairs := [M[1], M[2], ... , M[numelems(DeleteColumn(M, [1]))]];

with(CurveFitting):

PolynomialInterpolation(pairs, x);

Hi, I'm new to Maple and was trying to use it to solve 3 equations with 3 unknowns, in terms of another 2 parameters. This is what I put in, and the error that came up:

solve({(1-x)/(1+b) = b*y, (1-y)(1-a)/(-a*b+1) = b*z, (1-z)(1-b)/(-a*b+1) = a*x}, {x, y, z}); 

Error, (in SolveTools:-LinearSolvers:-Algebraic) unable to compute coeff

I want to solve the equations to get x,y,z in terms of a,b but I don't understand the error coming up - have I done something wrong or is it because not all the variables appear in all of the equations? As there are 3 equations and 3 unknowns there is a solution, but I want to check the answer I found on paper with something (the algebra got a bit messy!)

Any help greatly appreciated! :)

I am trying to simplify equation 18 using equations 8 and 9. It should look a little like equation 21, but instead I get the results in equations 19 and 20.  I tried using different substituions, but algsubs gets the closest answer. A few terms are going to zero after the substitution.

When I substitute Z(X) then Zbar(X) terms vanish, and visa versa.

Download Deriving_the_Kerr_Metric.mw

Hi,

I'm trying to create interactive plots by using Explore to help demonstrate the effects parameters have on functions. I created one successfully to illustrate shifts and stretches of a polynomial:

transform(A,B,X,H,P,K):=Explore(plot(a*(b*x+h)^(p)+k,x=X),parameters=[a=A, b= B,h=H,p=P,k=K],placement=right)

However when I try to do the same with a solved ODE it returns an error message:

Explore(plot(1/(-p*x+x+1)^(1/(p-1)), x = -5 .. 5), parameters = [p = -20 .. 20], placement = right);

Executing this gives the error message: 

Warning, expecting only range variable x in expression 1/((-p*x+x+1)^(1/(p-1))) to be plotted but found name p
INTERFACE_PLOT(AXESLABELS(x, ""),

VIEW(-5. .. 5., DEFAULT, _ATTRIBUTE("source" = "mathdefault"))),

parameters = [p = -20 .. 20], placement = right

I'm not sure why it is having difficulty dealing with "p" when it had no difficulty with the first. Any help would be appreciated!

Consider the problem of a hard-hit baseball. The air-friction drag on a baseball is approximately given by the following formula

and subsequent differential equations : 

F:=-((C_d)*rho*Pi*(r)^2*v*v)/2;
m:=0.145;
v0:=65;
g:=9.81;
v_x:=diff(x(t),t);
v_y:=diff(y(t),t);
d2v_x:=-((C_d)*rho*Pi*(r^2)*(v_x)*sqrt((v_x)^2 +(v_y)^2))/(2*m);
d2v_y:=-((C_d)*rho*Pi*(r^2)*(v_y)*sqrt((v_x)^2 +(v_y)^2))/(2*m)-g;

where

C[d] is the drag coefficient (about 0.35 for a baseball)

•
rho[air] is the density of air (about 1.2 kg/
3m
)
•
r is the radius of the ball (about 0.037 m)

v is the vector velocity of the ball

Then if given that : 

Power hitters in baseball say they would much rather play in Coors Field in Denver than in sea-level stadiums because it is so much easier to hit home runs. The air pressure in Denver is about 10% lower than it is at sea level. The field dimensions at Coors Field are:

Left Field - 347 feet (106 m)
Left-Center - 390 feet (119 m)
Center Field - 415 feet (126 m)
Right-Center - 375 feet (114 m)
Right Field - 350 feet (107 m)

 1. Overlay two plots: one at sea level and one in Denver to show why power hitters prefer Coors field.

2. Find the initial magnitude of velocity, v0

needed to hit a home run to Right-Center, where v_x(0)=v0/sqrt(2) and v_y(0)=v0/sqrt(2)

I don't quite understand how to use the field dimensions for both 1 and 2 and am pretty clueless as to how to approach this question using the ordinary differential equations mentioned above.

Hey guys, I'm new to the forum, so please tell if I need to set up the question in a different way :) I've tried to find an answer for this, but have struggled since our learning book is in danish, so the used terms may not be technically correct,

Anyways, how do you solve this problem in maple? 

Find the complete real solution for the differential equation system:

For the homogenous part I've found. (Is this correct?)

  , c1,c2 € R

I've tried to find an answer for the inhomogenous part but I get a really complicated result, so I doubt it's correct.

Thanks for the help :)

-Alex 

Is it possible to solve DDE with dsolve?

restart:

Eq1 := diff(x(t), t) = 1-.1*x(t)-0.5e-3*x(t)*v(t)/(1+0.1e-5*v(t));

Eq2 := diff(y(t), t) = 0.5e-3*x(t-10)*v(t-10)/(1+0.1e-5*v(t-10))-.3*y(t)-y(t)*z(t);

Eq3 := diff(v(t), t) = 200*y(t-10)-8*v(t);

Eq4 := diff(z(t), t) = 2*y(t)*z(t)-.15*z(t);

ics := x(0) = 1, y(0) = 1, v(0) = 5, z(0) = 1;

Thanks

I am trying to solve the Morrison equation for a normal force acting on a cylinder in a viscous fluid by using the potentional theory. With my limited experience in Maple I do not get why my dubble integral cannot be computed. Any help would be appreciated, tips are also very welkom as I am trying to expand my knowledge of Maple. 

Hi all,

I have lots of contstraint equations group and I want to fund a group of parameters which can fit them. 

For example, these are a simple constraint eqqations group:
eqs:{x1>0, x2>0 x1<1000, x2<1000, x1+x2>300,x1+x2<700}

Through SolveTools library, I can determine whether there is a group of parameters.

with(SolveTools[Inequality]);

LinearMultivariateSystem({x1 > 0, x1+x2 > 300, x2 < 1000, x1+x2 < 700, x2 > 0*x1 and 0*x1 < 1000}, [x1, x2]);

{[{x1 <= 300, 0 < x1}, {x2 < -x1 + 700, 300 - x1 < x2}],[{300 < x1, x1 < 700}, {0 < x2, x2 < -x1 + 700}]}

Then, if I want to find a group of parameter a group of parameters (ex, x1=300, x2=200 in this case), how should I do?

I've got the following four differential equations :

v_x:=diff(x(t),t);
v_y:=diff(y(t),t);
d2v_x:=-((C_d)*rho*Pi*(r^2)*(v_x)*sqrt((v_x)^2 +(v_y)^2))/(2*m);
d2v_y:=-((C_d)*rho*Pi*(r^2)*(v_y)*sqrt((v_x)^2 +(v_y)^2))/(2*m)-g;

and the following initial value conditions:

x(0)=0,y(0)=0,v_x(0)=v0/sqrt(2),v_y(0)=v0/sqrt(2) given v0=65 

I need to solve these using the numeric type and then draw overlaid plots

(i) setting C_d=0

(ii) leaving C_d as a variable

before plotting y(t) vs x(t). The hint for this last part is that the path can be seeing using [x(t),y(t)] instead of [t,y(t)]

I've tried to do it but seemed to have several syntax errors.

I've got the following diff.eq

y'(x)=sin(x*y(x)) given y(0)=1 

and need to solve it numerically which is why I've used:

dy4:=diff(y(x),x);
eqn4:=dy4=sin(x*y(x));
ic1:=y(0)=1;
ans3:=dsolve({eqn4,ic1},y(x),type=numeric);

This code doesn't return a value though and in fact, ans3 is being displayed as a procedure

"ans3:=proc(x_rkf45) ... end proc"

I don't quite understand why and what I need to do to get the required numerical solution