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These are replies submitted by Zeineb


thank you for your answer.

can we obtain a general solution without specify the vectors v[i] and for general n

@Axel Vogt 

I compare


  I see there is a difference between them



Thank you for your help

I use maple 18



@Carl Love 

The ODE is defined for all x in [o,1] except 1/2

The piecewise function is differentiable ( or piecewise differentiable) and it is derivative equal zero ( defined as piecewise function) so it is a solution


There are three solutions:

1) C1=C2

2) C1=-C2

3) C1 and C2 are orthogonal

the three cases give D1=D2


Thank you for the code.

We get that the vectors  C1  and  C2  either:
1) coincide or 
2) differ from each other by turning by an angle multiple of  90  degrees

And a  third case,

differ from each other by turning by an angle multiple of  180  degrees

@Thomas Richard 

Thank you for your remarks. There is another boundary condition


Its possible always to obtain an explicit solution

or can I plot always the numerical solution

many thanks


Thank you.

Can maple give a general  results using n

for each integer K and M from 0 to n-1

can we compute C(K).C(M)=..... the result depend on n and not for a fixed n

the same S(K).S(M)

and S(K).C(M)

Maybe can we find a general result.

Many thanks



K and M are in the set {0,1,2,...,n-1}

I hope if possible  compute for a given K and M the inner product between the two vectors C(K) and S(M)



Thank you

But I use the usual inner product of two vectors from R^n

<(a,b),(c,d)>=a.b +c.d


For fixed K and fixed M we compute the inner product



Rhanks. I have some remarks

for a<-3 the set solution is (-infinity, -a) and not (-infinity,zero]

for a>1 the set solution is emptyset

for -1<=a<0 the set solution is (0,1]

for -3<=a<-1 the set solution is (0,a)

What do you think about this answer


Thank you for your answer.

When we solve f(x)> a for example for  0<=a<=1 we obtain the set (sqrt(a),1) i.e. the solution must be an interval 

Because we have an inequality and not equality, so the solution as you show in the table must be many intervals in each case and this depend on value of a

@Christian Wolinski 


I would like use solve to get the set of solution of this inequation and my unknown is x and a is a paramter

@Christian Wolinski 

let a given

how can solve f(x) > a

Many cases will be discussed:

for example case 1) if a> 1  then f(x)> a has solution empty set

case 2:    0<=a<=1 , we solve f(x)>a

case 3 :


how can we get all cases using maple and maple solves f(x)>a

many thanks



Please Run this code, I would like see the solution if possible



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