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14-66 Computer Algebra System (CAS)
ILAP is the inverse Laplace transform of a given
expression. Again, the expression is the value of a
function of the variable stored in VX.
Laplace transform (LAP) and inverse Laplace transform
(ILAP) are useful in solving linear differential equations
with constant coefficients, for example:
The following relations hold:
where c is a closed contour enclosing the poles of f .
The following property is used:
The solution, y , of:
is then:
Example
To solve:
c
type:
LAP(X · EXP(3 · X))
The result is:
y
″
p y
′ ⋅
q y
⋅
+ + f x
( )
=
y 0
( )
a y
′
0
( )
b = =
LAP(y)(x) e
x – t
⋅
y t
( )
t d
0
+
∞
∫
=
ILAP(f)(x)
1
2 i
π
--------
e
zx
f z
( )
z d
c
∫
⋅
=
LAP y
′ ( )
x
( )
y 0
( )
– x LAP y
( )
x
( ) ⋅
+ =
y
″
p y
′ ⋅
q y
⋅
+ + f x
( )
, y 0
( )
a , y
′
0
( )
b = = =
ILAP
LAP f x
( ) ( )
x p +
( )
a b +
⋅
+
x
2
px q + +
-------------------------------------------------------------------
⎝ ⎠
⎛ ⎞
y
″
6 – y
′ ⋅
9 y
⋅
+ x e
3 x
⋅
, y 0
( )
a , y
′
0
( )
b = = =
1
x
2
6 x – 9 +
--------------------------
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