Respected member!
Please help me to find the solution of attached problem.

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Hi guys,

I'm trying to solve this system I have but the solution doesn't display:

-I have two second degree differential equations with two functions.

-I have a set of two boundary conditions per function.

Thank you!
 

Download trial.mwtrial.mw

This is reduced from another forum.

restart;
e1 := 12*g^2+12*h^2+4*i^2+3*j^2=684;
e2 :=  12*l^2+12*m^2+4*n^2+3*o^2=684;
e3 := 12*q^2+12*r^2+4*s^2+3*t^2=172;
e4 := 12*v^2+12*w^2+4*x^2+3*y^2=108;
e5 := 12*g*l+12*h*m+4*n*i+3*j*o=-84;
e6 := 12*g*q+12*h*r+4*s*i+3*j*t=-84;
e7 := 12*g*v+12*h*w+4*x*i+3*j*y=-84;
e8 := 12*l*q+12*m*r+4*n*s+3*o*t=-84;
e9 := 12*l*v+12*m*w+4*n*x+3*o*y=-84;
e10 := 12*q*v+12*r*w+4*s*x+3*y*t=-84;
e11 := g+h+i+j=-1;
e12 := l+m+n+o=-1;
e13 := q+r+s+t=-1;
e14 := v+w+x+y=-1;
e15 := h*i+m*n+3*s*r+4*x*w=-21;
e16 := g*i+l*n+3*s*q+4*x*v=-21;
e17 := i+n+3*s+4*x=-3;
e18 := g*h+m*l+3*q*r+4*w*v=-7;
e19 := h+m+3*r+4*w=-1;
e20 := g+l+3*q+4*v=-1;
e21 := i*j+o*n+3*s*t+4*x*y=-84;
e22 := j*h+o*m+3*r*t+4*y*w=-28;
e23 := j*g+o*l+3*q*t+4*y*v=-28;
e24 := j+o+3*t+4*y=-4;
e25 := j^2+o^2+3*t^2+4*y^2=144;
e26 := i^2+n^2+3*s^2+4*x^2=129;
e27 := h^2+m^2+3*r^2+4*w^2=57;
e28 := g^2+l^2+3*q^2+4*r^2=57;

eqset := {e1, e2, e3, e4, e5, e6, e7, e8, e9, e10, e11, e12, e13, e14, e15,
          e16, e17, e18, e19, e20, e21, e22, e23, e24, e25, e26, e27, e28};
for s in eqset do print(s) end do;

Error, too many levels of recursion

If I then do

S := {1,2,3,6,3,6,8,2,3,6};

for s in S do print(s) end do;

Then,

for s in eqset do print(s) end do;

has the correct output.

What am I doing wrong?

Tom Dean

Dear All

I have a trignometric function and I plotted it in 2D. It is visible from the graph that the function has Maxima and Minima. My question is, can I located all values
 

Download Max_Min_from_Graph.mw

of "x" corresponding to these Max. and Min. ?

dy/dx=sqrt(1+(a*x)+(2*y))

for the case a=1, y=1 and x=0 construct a program for the runge-kutta method of order 2 with formulae as follows where f(x,y)=dy/dx.

k_1=h*f(x_n,y_n)

k_2=h*f(x_n+h,y_n+k_1)

y_(n+1)=y_n+1/2(k_1+k_2).

After creating a program obtain value of y correct to 4 decimal places when x=1 for h=0.1 and h =0.05.

Meanwhile, thank you so much for everything.
I know I'm asking a lot but if you have time, you can help me do this?

Building a system of interactive components that, taken a function, two points 'a' and 'b' values ​​and an integer n, the calculations point between a and b in which the function assumes the minimum value by using the following procedure:

• It divides the values ​​between a and b into n equal parts (these will distance the one with the other (b-n)/2);
• calculates the function in each of these points;
• located between these values,  what is the minimum (in case of a tie, take the one closest to a)

I think i have to create a vector for each  part and  prehaps with a fcycle for, calculate the function, finelly i'll use minimize with all function.
Do you think is the correct procedure? If yes, how can I do it?

yVal := 0.01

xVal := 0.01

p8 := plot([fdiff(('rhs')((pds:-value(f(x, y)))(x, yVal)[3]), [y, y], x = z)], z = 0 .. 20, color = [red])

I cant seem to plot the graph for yVal, but if I were to switch it around to (xVal,y), the graph works perfectly. How should I input the code such that I can obtain the f''(x,0) graph. 

Any help will be greatly appreciated :) thanks

fyp3.mw

Dear All, 

I work on the period doubling phenomenon by integrating the dynamical system at some particular parameter values. My main commands are as follows

restart:
with(DEtools): with(plots): with(plottools):
a:=-1: b:=-3: c:=3: d:=1: omega:=1: v1:=1: f:=-4: epsilon:=0.01: 
sys:=diff(u1(t),t)=v1*u1(t)-(omega+u2(t)^2)*u2(t)+u1(t)*(a*(u1(t)^2+u2(t)^2)+b*z(t)^2),
     diff(u2(t),t)=(omega+u1(t)^2)*u1(t)+v1*u2(t)+u2(t)*(a*(u1(t)^2+u2(t)^2)+b*z(t)^2),
     diff(z(t),t)=z(t)*(-v1+c*(u1(t)^2+u2(t)^2)+z(t)^2)+epsilon*z(t)*(v2+f*z(t)^4):

solC:=dsolve({eval(sys, v2=2.0500014987),
              u1(0)=0.6,u2(0)=0.6,z(0)=0.1},
              type=numeric, method=rkf45, maxfun=10^7,
              range=350..750):
p1:=odeplot(solC, [sqrt(u1(t)^2+u2(t)^2),z(t)],
               refine=2,
               color=burgundy,
               thickness=1);
 

The resulting curves are quite blurring and furry. I have tried to increase the "refine" or the "numpoints" values, but with minimal improvement. I would like to know if there a way to obtain clean and sharp integral curves?  

I would be very grateful if someone could help me! 

Thank you in advance.

With kind wishes,

Wang Zhe

Hi, I try Aproximate integral with simpsons method, but i want value in function the a with number solution:

with(Student[Calculus1]);
ApproximateInt(a*tan(x)-2*x, x = -100 .. 100, method = simpson, output = plot, partition = 500);

This error.

How we can construct conservation laws of fractional differential equation with Maple?

Basically what I'm trying to do is use Newton's method to find the root of f(x)=sqrt(x)+ln(0.1x) starting at x0=5 within a tolerance of 0.001.

f := proc (x) options operator, arrow; sqrt(x)+ln(.1*x) end proc

> xk := 1.0;
print(`output redirected...`); # input placeholder
                              1.0
> for k to 6 do xk1 := xk-f(xk)/(D(f))(xk); xk := xk1 end do;
 

When I do that, Maple barfs out pages of nonsense when I'm looking for it to give numerical values. It seemed to work fine with a different function, so maybe that's part of the problem? But I need to do it with the function I asked about.

Respected member!
Please help me to find the solution of attached problem,  I am a new user so please forgive any mistakes.maple.mwmaple.mw

Hello,

I have been trying to solve a simple nonlinear equation. Im interested in the solution per say rather than the plot but when I browsed about the commands to use, this came up. I tried it in my case and it is giving me the following errors:

ode.mw
 

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The question explores the family of differential equations dy/dx = sqrt(1+(a*x)+(2*y)) for various values of the parameter a.

This figure shows the tangent field in the case a=1.

sketch a tangent field in the case a=-2.

need the following diagram on maple: