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
