HP 40gs User Manual
Page 248
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
2i
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
3x
⋅
, y 0
( )
a, y
′ 0
( )
b
=
=
=
1
x
2
6x
–
9
+
--------------------------
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