The ilaplace(M) calling sequence computes the element-wise inverse Laplace transform of M.  The result, R, is formed as R[i,j] = ilaplace(M[i,j], y, x).

ilaplace(L) is the inverse Laplace transform of the scalar L with default independent variable s.  If L is not a function of s, then L is  assumed to be a function of the independent variable returned by findsym(L,1).The default return is a function of t.

If L = L(t), then ilaplace returns a function of x.

By definition,

ilaplace(L,y) makes F a function of the variable y instead of the default t.

ilaplace(L,y,x) takes L to be a function of x instead of the default t. The integration is then with respect to y.