iLaplace(F(s), s)
Finds the Time function f(t) of the given Laplace function F(s).

Examples
iLaplace(10/p^(3/2), p)
20
t
π
iLaplace(b/sqrt(a*s), s)
b
a
t
π
iLaplace(b/(a*s)^5, s)
b
t
4
24
a
5
iLaplace(2/s+3/s^2-4/s^4, s)
-
2
t
3
3
+
3
t
+
2
iLaplace(-1/(-s-3)+(c^3)/s, s)
c
3
+
e
-
3
t
iLaplace(1/s+1/(s^2)-4/(s^3)-18/(s^4)+(-a)/(a^2+s^2)+(-s)/(a^2+s^2), s)
-
3
t
3
-
2
t
2
+
t
-
cos
(
a
t
)
-
sin
(
a
t
)
+
1
iLaplace(-288b*s^2/(b^2+s^2)^4+24b/(b^2+s^2)^3+384b*s^4/(b^2+s^2)^5, s)
t
4
sin
(
b
t
)
iLaplace(exp(k*sqrt(s)), s)
-
k
e
-
k
2
/
4
t
2
t
3
π
iLaplace(sqrt(3)exp(3/s)/(7sqrt(13)sqrt(s)), s)
3
cosh
(
2
3
t
)
7
13
t
π
iLaplace(sqrt(3)exp(3/s)/(sqrt(b)s*sqrt(s)), s)
3
sinh
(
2
3
t
)
b
3
π
iLaplace(exp(k/s), s)
k
BesselJ
(
1
,
2
-
k
t
)
-
k
t
+
Dirac
(
t
)
iLaplace(3*a*b*exp(a*sqrt(s)-b), s)
-
3
a
2
b
e
-
b
-
a
2
/
4
t
2
t
3
π
iLaplace(I(a/(s^3*(a^2+s^2)), s, 3), s)
-
1
a
3
t
3
+
1
2
a
t
+
cos
(
a
t
)
a
3
t
3
iLaplace(I(a/(a^2+s^2), s, 3), s)
sin
(
a
t
)
t
3
iLaplace(I(s/(a^2+s^2), s, 4), s)
cos
(
a
t
)
t
4
iLaplace(d(s/(s^2+1), s, 3), s)
-
t
3
cos
(
t
)
iLaplace(d(s/(s^2+1), s, -3), s)
cos
(
t
)
t
3
iLaplace(d(F(s), s, 2)+d(G(s), s, -3), s)
t
2
F
(
t
)
+
G
(
t
)
t
3
iLaplace(d(F(s), s, 3)+d(G(s), s, -3)+I(H(s), s, 3), s)
-
t
3
F
(
t
)
+
G
(
t
)
t
3
+
H
(
t
)
t
3

References

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