## ODE, infinite domain...

TQ.mw

Can any one help for finding the solution of these differntial equations and then plotting the graph for differnt values of M

(FILE ATTACHED)

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## Tangent Field in Maple...

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:

## How do I solve a complex equation in function of p...

Guys,

I am not very familiar with Maple and have to solve quite a complex equation.

I have an equation which is complex ,containing I . I split this equation up in Re=0 an Im=0 . I have to get an answer in function of other parameters, in order to plot these... Maybe it s easier if you look at the work sheet

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## numerical equation using loop for...

hello evrey one ,

my question is how can i solve numerical equation using loop

for each beta => deolve and export via excel
thank you

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## How to plot interactive vectors (or complex number...

I am quite a new user of Maple 2016.

I intend to plot complex numbers as vectors (Phasors), with diferent relationsships between them. I would like to use parameters and modify them e.g with a slider. I can't find how to do it.

For example:

V1=1*cos(delta)+j*sin(delta)

Ve=0.5*cos(alfa)+0.5*j*sin(alfa)

V2=Ve+V1

V2=1+j0

V12=V1-V2

I=V12/(Zcos(beta)+jZsin(beta))

I would like to be able to see those vectors, employing alfa and beta as parameters (e.g between -pi and pi)

Any ideas on how to plot that? Maybe Maple is not the right tool to do it. Is there any specific to plot interactive phasors?

Thanks

## Plot a path knowing x and y in function of a varia...

I need to plot a path with curvilinear coordinates. Knowing the curvature theta and length s of  parts that compose it, I found the equations of x and y as a function of the parameter s that goes from zero to the total length.
I make an example below:

for 0 <s <2,     x = s     and

y = 0 (straight line)

for 2 <s <2 + Pi,        x = 2 + 2 * sin ((s-2) / 2)      and

y = 2 * (1-cos ((s-2) / 2)

Now I want to find the corresponding plot of x (s), y (s) (without showing s as coordinate) but I do not know what commands I can use. Can you suggest me something? Thank you

## Parametric solution of polynomial system...

hi.

how i can solve two equation with respect to parameter sigma1

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## Problem with delta as parameter...

I want to ask., I put delta as my constant in maple program and I want the answer are in delta as well., but the thing is., when running., it let delta=0, delta=-1, and delta=delta.,
the condition is we cannot let delta=1 or delta=0 because it is just same for s5 and s7.,.(delta is refer to the s8). How can I get answer as delta? with the condition? here I attach my maple programme..

> derivation := proc (A, n)
local i, j, k, t, s5, s7, s8, m, D,
sols5, sols7, sols8, eqns5, eqns7, eqns8,
BChange5, BChange7, BChange8; eqns5 := {}; eqns7 := {}; eqns8 := {};
D := matrix(n, n);
BChange5 := matrix(n, n); BChange7 := matrix(n, n); BChange8 := matrix(n, n);
for i to n do for j to n do for m to n do
s5 := sum(0*A[i, j, k]*D[m, k], k = 1 .. n)-(sum(A[k, j, m]*D[k, i]+A[i, k, m]*D[k, j], k = 1 .. n));
s7 := sum(0*A[i, j, k]*D[m, k], k = 1 .. n)-(sum(A[k, j, m]*D[k, i]+0*A[i, k, m]*D[k, j], k = 1 .. n));
s8 := sum(0*A[i, j, k]*D[m, k], k = 1 .. n)-(sum(A[k, j, m]*D[k, i]+delta*A[i, k, m]*D[k, j], k = 1 .. n));
eqns5 := `union`(eqns5, {s5}); eqns7 := `union`(eqns7, {s7}); eqns8 := `union`(eqns8, {s8})
end do end do end do;
sols5 := [solve(eqns5)]; sols7 := [solve(eqns7)]; sols8 := [solve(eqns8)];
t := nops(sols5); t := nops(sols7); t := nops(sols8);
for i to t do for j to n do for k to n do
BChange5[k, j] := subs(sols5[i], D[k, j]);
BChange7[k, j] := subs(sols7[i], D[k, j]);
BChange8[k, j] := subs(sols8[i], D[k, j])
end do end do;
print("eqns&Assign;", eqns5); print("sols:=", sols5); print("BChange5:=", BChange5);
print("eqns&Assign;", eqns7); print("sols:=", sols7); print("BChange8:=", BChange7);
print("eqns&Assign;", eqns8); print("sols:=", sols8); print("BChange8:=", BChange8)
end do end proc;

> AS1 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 2) = 1]);
> derivation(AS1, 2);

> AS2 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (1, 2, 2) = 1]);
> derivation(AS2, 2);

> AS3 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (2, 1, 2) = 1]);
> derivation(AS3, 2);

> AS4 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (2, 2, 2) = 1]);
> derivation(AS4, 2);

> AS5 := array(sparse, 1 .. 2, 1 .. 2, 1 .. 2, [(1, 1, 1) = 1, (1, 2, 2) = 1, (2, 1, 2) = 1]);
> derivation(AS5, 2);

> AS1 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (3, 1, 2) = 1]);
> derivation(AS1, 3);

> AS2 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (3, 1, 2) = alpha]);
> derivation(AS2, 3);

> AS3 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 2) = 1, (1, 2, 3) = 1, (2, 1, 3) = 1]);
> derivation(AS3, 3);

> AS4 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (2, 3, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS4, 3);

> AS5 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(2, 3, 2) = 1, (3, 1, 1) = 1, (3, 3, 3) = 1]);
> derivation(AS5, 3);

> AS6 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(3, 1, 2) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS6, 3);

> AS7 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 2, 1) = 1, (2, 2, 2) = 1, (3, 1, 1) = 1, (3, 3, 3) = 1]);
> derivation(AS7, 3);

> AS8 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 1) = 1, (2, 3, 2) = 1, (3, 1, 1) = 1, (3, 3, 3) = 1]);
> derivation(AS8, 3);

> AS9 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(2, 3, 2) = 1, (3, 1, 1) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS9, 3);

> AS10 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 1) = 1, (2, 3, 2) = 1, (3, 1, 1) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS10, 3);

> AS11 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 3, 2) = 1, (2, 3, 2) = 1, (3, 1, 2) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS11, 3);

> AS12 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 2) = 1, (1, 3, 1) = 1, (2, 3, 2) = 1, (3, 1, 1) = 1, (3, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS12, 3);

> AS13 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS13, 3);

> AS14 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 2, 1) = 1, (2, 1, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS14, 3);

> AS15 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 2, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS15, 3);

> AS16 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(2, 1, 1) = 1, (2, 2, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS16, 3);

> AS17 := array(sparse, 1 .. 3, 1 .. 3, 1 .. 3, [(1, 1, 2) = 1, (3, 3, 3) = 1]);
> derivation(AS17, 3);
>

## Bounded solution of ODE...

Dear all

I have the following equaion

Eq := diff(phi(x, k), x, x)+(k^2+2*sech(x))*phi(x, k) = 0;

The solution is given by

phi := (I*k-tanh(x))*exp(I*k*x)/(I*k-1);

My question : At what value of k is there a bound state and in this case can we give a simple form of the solution phi(x,k)

With best regards

## Numerically solving parametric integral...

Hello everyone,

I am trying to solve numerically int( f(t,z) , t=0..T ) = 0 , in z for a cumbersome f.

I tried z1=fsolve( int( f(t,z) , t=0..T ) = 0 , z). But then I tried int( f(t,z1) , t=0..T ) and the result is clearly not zero nor anything small.

It looks like Maple evaluates analytically the integral, and does it wrong (check this for more details) so fsolve uses the wrong equations.

Anyone knows how I can force Maple to evaluate numerically the integral at each step of the fsolve function?

Thank you!

## Equation with parametric integral ...

I want to solve one equation with one variable and the variable is also in definite integral delimiter. When trying fsolve, I get the error:

"Error, (in fsolve) Can't handle expressions with typed procedures"

Here is worksheet.mw

How can I obtain solution with method other from simple manual testing Te values?

## Problem with solving...

I have a problem with finding a interval where parametr "a" is changing.
My funcion:

exp(x2(a-x)) for xcR.
I did this, and I don't know what's next.

g:=x->exp(x2(a-x));
dg:=diff(g(x),x);
solve(dg=0,x);
0,2/3a
g(0);
g(2/3a);

I am solving a complicated ODE and I would like to know if there is a way for Maple to output the ODEs without doing any numerical substitutions for known parameters. Say one of my parameters, call it P, is initialized (there are many more but Ill just simplify and consider one here) to a value of 10. In order to chekc that I have coded the ODEs correctly it would help me if Maple does not substitue with the numerical value 10 for P when displayng teh ODEs, but rather keeps P, as a parameter. Is there a way to achieve this?

## Relation between parameters...

I have written the following coade in Maple:
r := 50;
l1 := 0.2742e-10;
s := I*w;
l := (-1.342110665*10^22*c^2*(Pi^4)-4.225000000*10^25*c^2*(Pi^2)+2.316990000*10^11*c1*(Pi^2)-1)/(-1.342110665*10^22*c^2*c1*(Pi^4)-7.140250000*10^43*c^2*c1*r^2*(Pi^4)+1.957856550*10^33*c^2*(Pi^4)+9.789282750*10^32*c*c1*(Pi^4)-1.690000*10^22*c*(Pi^2)-4.22500*10^21*c1*(Pi^2));
z1 := (c*l1*s^2+1)/(c*s);
z2 := l*s/(c1*l*s^2+1);
h := (z1+2*z2)*((z1+2*r)*(z1+3*z2)/(2*r)-2*z2)/z2-(1/2)*z2*(z1+2*r)*r;
f := h*(z1+3*z2)/z2-(z1+2*r)(2*r)*(z1+3*z2)+2*z2;
gain := 2*z2/f;
a := abs(gain);
d := diff(a, w);
s := subs(w = 2*pi*0.325e11, d)
Now, I have a function named "s" which I want to set to zero, and calculate the relationship between variables c & c1 in order to achieve this. How should it be done?
Thanks.