ilaplace

Description

ilaplace(F,trans_var,eval_point) computes the inverse Laplace transform of F with respect to the transformation variable trans_var at the point eval_point.

Input Arguments

Examples

Compute the inverse Laplace transform of this expression with respect to the variable y at the evaluation point x:

syms x y
F = 1/y^2;
ilaplace(F, y, x)

ans =
x

Compute the inverse Laplace transform of this expression calling the ilaplace function with one argument. If you do not specify the transformation variable, ilaplace uses the variable s:

syms a s x
F = 1/(s - a)^2;
ilaplace(F, x)

ans =
x*exp(a*x)

If you also do not specify the evaluation point, ilaplace uses the variable t:

ilaplace(F)

ans =
t*exp(a*t)

Compute the following inverse Laplace transforms that involve the Dirac and Heaviside functions:

syms s t
ilaplace(1, s, t)

ans =
dirac(t)

ilaplace(exp(-2*s)/(s^2 + 1) + s/(s^3 + 1), s, t)

ans =
heaviside(t - 2)*sin(t - 2) - exp(-t)/3 +...
(exp(t/2)*(cos((3^(1/2)*t)/2) + 3^(1/2)*sin((3^(1/2)*t)/2)))/3

If ilaplace cannot find an explicit representation of the transform, it returns an unevaluated call:

syms F(s) t
f = ilaplace(F, s, t)

f(t) =
ilaplace(F(s), s, t)

laplace returns the original expression:

laplace(f, t, s)

ans(s) =
F(s)