ilaplace - Inverse Laplace transform

Syntax

F = ilaplace(L) F = ilaplace(L,y) F = ilaplace(L,y,x)

Description

F = ilaplace(L) is the inverse Laplace transform of the scalar symbolic object L with default independent variable s. The default return is a function of t. The inverse Laplace transform is applied to a function of s and returns a function of t.

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

F = F(x)

By definition

where c is a real number selected so that all singularities of L(s) are to the left of the line s = c, i.

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

Here y is a scalar symbolic object.

F = ilaplace(L,y,x) takes F to be a function of x and L a function of y instead of the default variables t and s, respectively.

Examples

Inverse Laplace Transform	MATLAB Command
= t	syms s; f = 1/s^2; ilaplace(f) returns ans = t
= xe^ax	syms a t; g = 1/(t-a)^2; ilaplace(g) returns ans = xexp(ax)
	syms x u; syms a real; f = 1/(u^2-a^2); simplify(ilaplace(f,x)) returns ans = sinh(a*x)/a

Inverse Laplace Transform

MATLAB Command

= t

syms s;
f = 1/s^2;
ilaplace(f)

returns

ans =
t

= xe^ax

syms a t;
g = 1/(t-a)^2;
ilaplace(g)

returns

ans =
x*exp(a*x)

syms x u;
syms a real;
f = 1/(u^2-a^2);
simplify(ilaplace(f,x))

returns

ans =
sinh(a*x)/a

ilaplace - Inverse Laplace transform

Syntax

Description

Examples

See Also

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