I get a problem while selecting elements from sets.

I have a list of two sets apparently ordered in the same order.
When I pick this, for instance, first set from each of these two samples I get the first one from the first set, and the second one from the second set.

Download Selection_from_a_set.mw

Running this command

map(sort, LDF)

displays LDF, which suggests that LDF is already sorted according to some order.
What is this order which makes diff(Theta(x), x$2) the successor of diff(Theta(x), x)  but diff(g(x), x) the successor of diff(g(x), x$2)  ?

When you use

restart:
with(Physics):
Setup(mathematicalnotation=true):
diff(x(t), t)

the output is $\dot{x}(t)$
When you write 

restart:
alias(x=x(t)):
diff(x, t)

the output is $\frac{\partial}{\partiall t} x$

Is it possible to "mix" these two in such a way that diff(x, t) appears as $\dot{x}$ ?
Notation.mw

Thanks in advance

Not the first time that a question (OP's name  PhearunSeng ) is removed as I am writing an answer (I guess other people have already faced the same inconvenience). 
Why doesn't exist a mechanism which prevents removing, deleting, displacing a question where someone (here Carl) has akready given an answer ???

Whatever the reason, here is my answer

Title: Can be done quickly if you write the matrix in a more abstract form

MyKGff := Matrix(5, 5, 
  {
    (1, 1) = A+(1/63368)*B, 
    (1, 2) = -(1/63368)*B, 
    (1, 3) = -(1/39605)*B, 
    (1, 4) = 0, 
    (1, 5) = 0, 
    (2, 1) = -(1/63368)*B, 
    (2, 2) = (1/63368)*B+C, 
    (2, 3) = (1/39605)*B, 
    (2, 4) = -C, 
    (2, 5) = 0, 
    (3, 1) = -(1/39605)*B, 
    (3, 2) = (1/39605)*B, 
    (3, 3) = (8/198025)*B, 
    (3, 4) = 0, 
    (3, 5) = 0, 
    (4, 1) = 0, 
    (4, 2) = -C, 
    (4, 3) = 0, 
    (4, 4) = C+(1/63368)*F, 
    (4, 5) = -(1/39605)*F, 
    (5, 1) = 0, 
    (5, 2) = 0, 
    (5, 3) = 0, 
    (5, 4) = -(1/39605)*F, 
    (5, 5) = (8/198025)*F
  }
);

Then (Maple 2015.2)

PseudoInverse := CodeTools:-Usage( LinearAlgebra:-MatrixInverse(MyKGff, method=pseudo) ):
memory used=28.38MiB, alloc change=68.00MiB, cpu time=312.00ms, real time=314.00ms, gc time=24.90ms

To recover the pseudo inverse with original data do

Rewrite := [
             A = (D__pile*W[1] . E__c)/3000, 
             B = (D__pile*W[2] . E__c)*89^(1/2), 
             C = (D__pile*W[3] . E__c)/1000, 
             F = (D__pile*W[4] . E__c)*89^(1/2)
           ]:

eval(PseudoInverse, Rewrite):

InverseMatrix_mmcdara.mw

@ASHAN's question was about a linestyle which wasn't displayed as expected.

Maybe a handling error on my part?

To ASHAN:

• Answer to your question here Help_graph_style_mmcdara.mw
• Extra: formal solution to the ODE here ODE_Formal_Solution.mw

Does anyone have any idea why Maple can obtain a closed form of 

Int(f, t=1..3);

but doesn't for 

Int(g, t=1..3);

?

The Int forms are quite close and I don't understand what makes Maple's task that difficult in the second case (the issue seems to come from the conditions in the piecewise function).
Can we force Maple to perform the second integration ?

TIA

Download MyIntegral.mw