# I'm trying to substitute a value in a Laplace transform

Hello, I'm trying to solve a DE by using Laplace transforms, but when I get the lapalce transfrom of my DE I get this part s*D0(0) and I don't know how can I substitute D[0], I tried D0(0) == -1) but I get an error that says that D is not defined, I can subs y(0) == 1 with no issues. So my question is how can I substitute the value for y'(0)=-1 in the Laplace transform.

thank you for your help !.

t = var('t')
s = var('s')
y = function('y')(t)

ED = diff(y,t,2)-2*diff(y,t)-3*y==4

ED_Lap = ED.laplace(t,s)
ED_Lap = solve(ED.laplace(t,s),laplace(y(t), t, s))
print(ED_Lap)
show(ED_Lap[0].rhs().subs(y(0)==1,D[0](y)(0)==-1).inverse_laplace(s,t)) # I don't know how to subs D

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In fact, D[0](y) is one way to represent diff(y, t).

So just do:

sage: ED_Lap[0].rhs().subs(y(0)==1,diff(y, t)(0)==-1).inverse_laplace(s,t)
1/3*e^(3*t) + 2*e^(-t) - 4/3

more

Thank you very much for your time. Now it works !! :D

( 2018-11-27 13:39:45 -0500 )edit

Glad this helped. Please formally accept the answer by clicking the "accept" button (the one with a tick sign). This way the question will be marked as solved in the list of questions.

( 2018-11-28 00:39:21 -0500 )edit