HP 40gs - 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″ py′⋅ qy⋅++ fx()=
y 0() a y′ 0() b==
LAP(y)(x) e
x– t⋅
yt() td
0
+
∞
∫
=
ILAP(f)(x)
1
2iπ
--------
e
zx
fz()zd
c
∫
⋅=
L
AP y′()x() y 0()– x LAP y()x()⋅+=
y″ py′⋅ qy⋅++ fx(), y 0() a, y′ 0() b===
ILAP
LAP fx()()xp+()ab+⋅+
x
2
px q++
-------------------------------------------------------------------
⎝⎠
⎛⎞
y″ 6– y′⋅ 9 y⋅+ xe
3x
⋅ , y 0() a, y′ 0() b===
1
x
2
6x–9+
--------------------------
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