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

Examples
Laplace(exp(a*t)+c^3-t^2, t)
-
2
s
3
+
c
3
s
+
1
-
a
+
s
Laplace(1+t-2t^2-3t^3-sin(a*t)-cos(a*t), t)
1
s
+
1
s
2
-
4
s
3
-
18
s
4
-
a
a
2
+
s
2
-
s
a
2
+
s
2
Laplace(t^4*sin(a*t)+sin(b*t)^3, t)
-
288
a
s
2
(
a
2
+
s
2
)
4
-
3
b
4
(
9
b
2
+
s
2
)
+
3
b
4
(
b
2
+
s
2
)
+
24
a
(
a
2
+
s
2
)
3
+
384
a
s
4
(
a
2
+
s
2
)
5
Laplace(exp(a*t)*sinh(b*t)^3, t)
-
3
b
4
(
-
b
2
+
(
-
a
+
s
)
2
)
+
3
b
4
(
-
9
b
2
+
(
-
a
+
s
)
2
)
Laplace(1/sqrt(#pi*t)-1/sqrt(t^3)+sqrt(a*t^3), t)
1
s
+
3
a
π
4
s
5/2
+
2
s
π
Laplace((exp(b*t)-exp(a*t))/(2sqrt(#pi*t^3)), t)
-
-
b
+
s
+
-
a
+
s
Laplace(-6exp(-4t)-3exp(-t)+9exp(-2t), t)
-
6
s
+
4
-
3
s
+
1
+
9
s
+
2
Laplace(t^2*exp(-a*t)/2, t)
1
(
a
+
s
)
3
Laplace(Heaviside(t-3)*sin(c*(t-3)), t)
c
e
-
3
s
c
2
+
s
2
Laplace(BesselJ(0, a*t)+BesselJ(0, 2sqrt(k*t)), t)
e
-
k
/s
s
+
1
a
2
+
s
2
Laplace(BesselJ(1, a*t), t)
a
(
s
+
a
2
+
s
2
)
a
2
+
s
2
Laplace(BesselI(1, a*t), t)
s
-
-
a
2
+
s
2
a
-
a
2
+
s
2
Laplace(Erf(a*t), t)
-
Erf
s
2
a
+
1
e
s
2
/
4
a
2
s
Laplace(Erf(a*sqrt(t)), t)
a
s
a
2
+
s
Laplace(Erfc(a*sqrt(b*t)), t)
1
s
-
a
b
s
s
+
a
2
b
Expand(Laplace((t+3)^(3/2), t))
-
3
π
Erf
(
3
s
)
e
3
s
4
s
5/2
+
(
3
s
)
3/2
2
s
7/2
+
3
π
e
3
s
4
s
5/2
+
(
3
s
)
3/2
s
5/2
Laplace(f(t)/t, t)
I
(
f
(
s
)
,
s
)
Laplace(t^3*f(t), t)
-
f'''
(
s
)
Laplace(R*i(t)+L*d(i(t), t)=u(t), t)
-
u
(
s
)
+
L
(
-
i
(
0
)
+
s
i
(
s
)
)
+
R
i
(
s
)
Solve_Equation(Laplace(R*i(t)+L*d(i(t), t)=u(t), t), I(s))
-
L
i
(
0
)
-
u
(
s
)
+
R
i
(
s
)
+
L
s
i
(
s
)
Laplace(f(t)*sin(3t), t)
Convolution
f
(
s
)
,
3
s
2
+
9
Laplace(t^4*f(t)*sin(3t), t)
D
D
D
D
Convolution
f
(
s
)
,
3
s
2
+
9
,
s
,
s
,
s
,
s
Laplace(f(t)*cos(2t)/t, t)
I
Convolution
f
(
s
)
,
s
s
2
+
4
,
s
Laplace(R*i(t)+1/C*I(i(t), t)=U, t)
-
U
s
+
R
i
(
s
)
+
i
(
s
)
C
s
Solve_Equation(Laplace(R*i(t)+1/C*I(i(t), t)=U(t), t), I(s))
-
U
(
s
)
+
R
i
(
s
)
+
i
(
s
)
C
s

References

Related Functions
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
Q
R
S
T
V
W
Z