I was going to do simply

int(Dirac(x)*exp(t-x), x = -infinity .. t) assuming t>0

The only reason I started with t=0 was to conform ot the theorem of convolution.

Thanks

 Sorry for the wrong name. Thanks Georgios!

 Yes I know it was not that clear.  Next time, I will put extra time to be sure that it will be readable not just for me but others.

 far from the answer I get by hand.  Here's my worksheet.

laplace.mw

 You will see below what is happening.

As you can see, x(t) and x'(t) does not update.

 I simply did a copy and paste of your last post.  I use Maple 12.01.  Here the result

> deq := diff(x(t), t, t)+2*(diff(x(t), t))-5*x(t) = 0; ci := x(0) = 1, (D(x))(0) = -2; p := dsolve({ci, deq}, x(t), numeric, range = 0 .. 5, output = Array([`$`(.1*j, j = 0 .. 50)]));

                      /  2      \                            
                      | d       |     / d      \             
               deq := |---- x(t)| + 2 |--- x(t)| - 5 x(t) = 0
                      |   2     |     \ dt     /             
                      \ dt      /                            
                        ci := x(0) = 1, D(x)(0) = -2
Warning, argument #6, the integer data must be at least 28 in size
                            [  [          d      ]   ]
                            [  [t, x(t), --- x(t)]   ]
                            [  [          dt     ]   ]
                            [                        ]
                       p := [[ 51 x 3 Matrix        ]]
                            [[ Data Type: anything  ]]
                            [[ Storage: rectangular ]]
                            [[ Order: Fortran_order ]]

Sorry.  I don't have a clue.  It's a bug bug since it work fine in Maple 11.01.  I will report it!  Thanks for your time on this.

the time "t" evaluate correctly but the value x(t) and x'(t) does not increment .  Eventhough I copy and paste your command?

> p:= dsolve({deq,ci},x(t),numeric, range=0..5, output= Array([0.1*j $ j=0..50]));
Warning, argument #6, the integer data must be at least 28 in size

 Suppose I have

> deq := diff(x(t), t, t)+2*(diff(x(t), t))-5*x(t) = 0;

                      /  2      \                            
                      | d       |     / d      \             
               deq := |---- x(t)| + 2 |--- x(t)| - 5 x(t) = 0
                      |   2     |     \ dt     /             
                      \ dt      /                            
> ci := x(0) = 1, (D(x))(0) = -2;

                        ci := x(0) = 1, D(x)(0) = -2
> p:= dsolve({deq,ci},x(t),numeric, range=0..5, output= Array([[0.1*j $ j=0..50],));

Warning, argument #6, the integer data must be at least 28 in size
                            [  [          d      ]   ]
                            [  [t, x(t), --- x(t)]   ]
                            [  [          dt     ]   ]
                            [                        ]
                       p := [[ 28 x 3 Matrix        ]]
                            [[ Data Type: anything  ]]
                            [[ Storage: rectangular ]]
                            [[ Order: Fortran_order ]]

If I look at the 28 x 3 Matrix, the time "t" evaluate correctly but the value x(t) and x'(t) does not increment.  And I have no clue about the warning message.  Where the 28 come from?

 Thanks in advance

First, remove the  "print(`output redirected...`); # input placeholder" living it empty (blank paragraph)

then highlight the input AND output of Maple that you paste.  Choose in the menu above the format wich will be "formatted".  Everything will look more readable for us to help you.

The rest of the text will be format as Normal

 that the first column will be <a,b,c,d> and the next <0,0,0,1> and so on.

> M(1 .. , 1) := <a, b, c, d>;

                                   [a  0  0  0]
                                   [          ]
                                   [b  0  0  0]
                              M := [          ]
                                   [c  0  0  0]
                                   [          ]
                                   [d  2  3  4]
 

It does not add a column.  Any idea?