HP 50g User Manual Page 497

Graphing calculator.

Note: Using the two examples shown here, we can confirm what we indicated
earlier, i.e., that function ILAP uses Laplace transforms and inverse transforms to
solve linear ODEs given the right-hand side of the equation and the
characteristic equation of the corresponding homogeneous ODE.
Example 3 – Consider the equation
where (t) is Dirac's delta function.
Using Laplace transforms, we can write:
With '
Delta(X-3)
–3s
= e
. With Y(s) = L{y(t)}, and L{d
and y
= h'(0), the transformed equation is s
1
the calculator to solve for Y(s), by writing:
The result is
To find the solution to the ODE, y(t), we need to use the inverse Laplace
transform, as follows:
ƒ ƒ
OBJ
μ
ILAP
The result is
2
d
y/dt
2
L{d
y/dt
2
L{d
y/dt
' ` LAP , the calculator produces EXP(-3*X), i.e., L{ (t-3)}
'X^2*Y-X*y0-y1+Y=EXP(-3*X)' ` 'Y' ISOL
'Y=(X*y0+(y1+EXP(-(3*X))))/(X^2+1)'.
'y1*SIN(X)+y0*COS(X)+SIN(X-3)*Heaviside(X-3)'.
2
+y = (t-3),
2
+y} = L{ (t-3)},
2
} + L{y(t)} = L{ (t-3)}.
2
2
2
y/dt
} = s
Y(s) - s y
2
Y(s) – s y
Isolates right-hand side of last expression
Obtains the inverse Laplace transform
– y
, where y
o
1
–3s
– y
+ Y(s) = e
o
1
Page 16-20
= h(0)
o
. Use  