## 135 Reputation

3 years, 228 days

## is there a general solution...

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

## expand...

I compare

and

I see there is a difference between them

## maple 18...

Thank you for your help

I use maple 18

## @Carl Love  The ODE is defined for...

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

## three cases...

There are three solutions:

1) C1=C2

2) C1=-C2

3) C1 and C2 are orthogonal

the three cases give D1=D2

## also: differ from each other by turning ...

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

## a more boundary condition...

Thank you for your remarks. There is another boundary condition

u(x,1)=3;

Its possible always to obtain an explicit solution

or can I plot always the numerical solution

many thanks

## @dharr  Thank you. Can maple give...

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

## @Zeineb    K and M are in th...

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)

## @Kitonum  Thank you But I use the...

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

## @Ramakrishnan  Rhanks. I have some...

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)

## @Ramakrishnan Thank you for your an...

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  Inequation.mw...

Inequation.mw

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 ...

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 :

etc

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

many thanks

## @Zeineb  Please Run this code, I w...

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

Run_code.mw

Thanks

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