## How to solve DE with initial conditions?...

I have a equation f(x) = 0.8680555556e-1*x*(3.262720*x^5*n[2]-.63360*x^5*n[1]^2+2.69184*x^5*n[1]-.480*x^3*n[1]^2+2.5920*x^3*n[2]+5.760*n[1]*x+1.920*n[2]*x^2+0.96e-1*x^4*n[1]^3+3.04320*x^4*n[2]-.5280*x^4*n[1]^2-0.32e-1*x^5*n[1]^4+.2976*x^5*n[1]^3-.1184*x^5*n[2]^2+.5376*x^5*n[3]-0.576e-1*x^4*n[1]+.576*x^4*n[3]-6.3360*x^3-6.96960*x^4-7.349760*x^5+11.520-.192*x^5*n[1]*n[3]-.7104*x^4*n[1]*n[2]+.2528*x^5*n[1]^2*n[2]-1.81824*x^5*n[1]*n[2])

with condition  f(0)=0,f'(0)=1;

How to solve this equation and how to find unknown parameters n[1],n[2],n[3]?

## How to write this equation in maple?...

How to write this equation in maple?

g(k-r-1);

conditions:=

1.r from 0 to k,

2.g(0)=1;

3.g(n)=0, where n not equal to 0.

## Collect / Common Factoring...

Hey guys, I'm a new Maple user and I've been struggling to figure the collect command out.

I made a smaller example to show what I am looking for

I want to find out a way to use collect command and go from "c" output to "d", choosing the terms I want to be collected as common factors.

I'm also uploading the files if it's of any help, The one called question is the example in the picture above and final objeticve is the big expression that I`m trying to factor.

In the final objective file I'm looking for a way to make the "i" output be factored like this as:

Wi δ Wi (...) + Wi δ Wf (...) + Wi δ θi (...) + Wi δ θf (...) + Wf δ Wf (...) + Wf δ Wi (...) + Wf δ θi (...) + Wf δ θf (...) + ...

## Computing radius and centers of disjoing balls...

Hi!

Assume that we have, in the cube C:=[-1,1]^N, for a fixed integer N>=2, a point X1  and   cosider the (closed) ball centered at X1 and radius R1:=0.6. Fixed an integer m>2, Somebody can indicate me how to compute the centers (belonging to C) and the radius of m disjoint balls with the above ball?

That is to say, compute points X2,...,Xm (in C) and positive numbers R2,...,Rm such that the intersection of the (closed) balls B(Xj,Rj) for j=1,...,m be empty.

Some suggestion?

## Differentiation of a matrix...

Dear Users,

I have a set of linear equations which can be presented as A(alpha,n) x(alpha)=b(alpha,n), where 'n' is the dimension of the square matric A.

For a particular value of "n" and "alpha", I can solve the unknown vector x. Further, I can differentiate Ax=b with respect to alpha to find out the rate of change of variable x with respect to alpha.

The above exercise reads, Ax'=b'-xA', which gives the unknown vector x', for a given value of alpha and n.

If I chose different values of n while fixing alpha=alpha0, the rate of change of x with alpha ( x' ) does not converge with 'n'. I noticed that x (alpha=alpha0) converges with n, also x(alpha=alpha0+ delta alpha) also converges with 'n'. I am interested in the query why x' does not converge, in spite of the fact that x converges? Any comments regarding the same are highly appreciated.

Thanks,

Grv

## finding binomial factors...

Hi MaplePrimes,

I'm trying to explore the polynomial r = n^2+n+39.  where n is an integer

I want restrictions on n such that r will factor into two trinomials.

Here is how far I got -

prime_poly_39_explore.mw

The 'has' function may be helpful.

Any help is appreciated.

Regards,

Matt

## Subsindets/evalindets fail recurse, is this a bug?...

I believe this is a bug:

```
(((Q(a)^3)^(5/4))^(15/7))^(6/8);
subsindets(%, anything^rational, proc(x) if type(x, specfunc(anything, Q)^rational) then 'Q(x)' else 'x' fi end)<>
subsindets(%, specfunc(anything, Q)^rational, Q);
```

## Cloud problem. ...

Why am I not able to use my MaplePrimes login credentials to login into MapleCloud?

Hi!

I am very interested in using the "phc.module", which is a module to work with "polynomial homotopy continuation" method. Please, see this paper

I have downloaded the following files: [copied without permission, deleted by moderator]

Then, I open (as an "ordinary" maple worksheet) the file "phc_savelib.maple" and execute it, but it seems that I can not use their functions and procedures because it returns errors.

For instance, follwing the attached PDF,  in the phc_savelib.maple file, define the polynomial system:

T := makeSystem([x, y], [], [x^2+y^2-1, x^3+y^3-1])

and try to solve the above system

sols := solve(T)

but returns the error

Error, (in fopen) file or directory does not exist

## evaluting integral with real and imaginary part ...

Hi all, I want to evaluate the integral G2. I am using the evalf command, but maple is unable to evaluate it. What am I missing here?

G2 := -.5*(int(Re(-(0.8823529412e-2*(-16.19435640-30.82287308*exp(-.2960360476-(1.*I)*theta)))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta))))*(-.5*cos(.3926990818+.5*theta)*sin(-.3926990818+.5*theta)+.5*sin(.3926990818+.5*theta)*cos(-.3926990818+.5*theta))/sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))-0.1764705882e-1*sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))*(1.017602550-3.872635115*exp(-.2960360476-(1.*I)*theta))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta))))-0.1764705882e-1*sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))*(-16.19435640-30.82287308*exp(-.2960360476-(1.*I)*theta))*(-0.6282080040e-1-(0.6282080040e-1*I)*(.5*cos(-.3926990818+.5*theta)/sin(.3926990818+.5*theta)+.5*sin(-.3926990818+.5*theta)*cos(.3926990818+.5*theta)/sin(.3926990818+.5*theta)^2)*sin(.3926990818+.5*theta)/sin(-.3926990818+.5*theta))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta)))))*(-.5-.5*cos(2.*theta))+.5*Im(-(0.8823529412e-2*(-16.19435640-30.82287308*exp(-.2960360476-(1.*I)*theta)))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta))))*(-.5*cos(.3926990818+.5*theta)*sin(-.3926990818+.5*theta)+.5*sin(.3926990818+.5*theta)*cos(-.3926990818+.5*theta))/sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))-0.1764705882e-1*sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))*(1.017602550-3.872635115*exp(-.2960360476-(1.*I)*theta))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta))))-0.1764705882e-1*sqrt(-1.*sin(.3926990818+.5*theta)*sin(-.3926990818+.5*theta))*(-16.19435640-30.82287308*exp(-.2960360476-(1.*I)*theta))*(-0.6282080040e-1-(0.6282080040e-1*I)*(.5*cos(-.3926990818+.5*theta)/sin(.3926990818+.5*theta)+.5*sin(-.3926990818+.5*theta)*cos(.3926990818+.5*theta)/sin(.3926990818+.5*theta)^2)*sin(.3926990818+.5*theta)/sin(-.3926990818+.5*theta))*exp(.1480180238-(1.*I)*(.5*theta-0.6282080040e-1*ln(-1.*sin(-.3926990818+.5*theta)/sin(.3926990818+.5*theta)))))*sin(2.*theta), theta = 0. .. .7853981635))

## Solve equations...

I'm trying to solve this to set of equations :

```EQ1:=-1958143.922*k*wr+2468.8339*k^3*wr-0.9481118254e16*k^2-114000.8376*k^4:

EQ2 :=-1186578.220*R*k^2*wr-312683.0293*k^5-288960.9621*k^3*R:
```

using a loop for different value of R in the range this range (wr=0..10,k=0..10)

```eqns:={EQ1,EQ2}:
for i from 1 by 1 to 101 do R:=(i-1):S:=fsolve(eqns,{k, wr},{wr=0..10,k=0..10}):v(i):=(subs(S,(wr)));w(i):=(subs(S,(k)))end do:
```

but i get this instead :

```Error, invalid input: subs received fsolve({-312683.0293*k^5, -1958143.922*k*wr+2468.8339*k^3*wr-0.9481118254e16*k^2-114000.8376*k^4}, {k, wr}, {k = 0 .. 10, wr = 0 .. 10}), which is not valid for its 1st argument
```

is there another way to solves this equations more easly .

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