# HP 48gII User Manual Page 499

Graphing calculator.

' ` LAP , the calculator produces EXP(-3*X), i.e., L{δ(t-3)}
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:
'X^2*Y-X*y0-y1+Y=EXP(-3*X)' ` 'Y' ISOL
The result is
'Y=(X*y0+(y1+EXP(-(3*X))))/(X^2+1)'.
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
'y1*SIN(X)+y0*COS(X)+SIN(X-3)*Heaviside(X-3)'.
Notes:
[1]. An alternative way to obtain the inverse Laplace transform of the
expression '(X*y0+(y1+EXP(-(3*X))))/(X^2+1)' is by separating the
expression into partial fractions, i.e.,
'y0*X/(X^2+1) + y1/(X^2+1) + EXP(-3*X)/(X^2+1)',
and use the linearity theorem of the inverse Laplace transform
-1
L
{a⋅F(s)+b⋅G(s)} = a⋅L
to write,
-1
⋅s/(s
L
{y
o
-1
⋅L
y
{s/(s
o
Then, we use the calculator to obtain the following:
2
2
L{d
y/dt
} + L{y(t)} = L{δ(t-3)}.
2
2
2
⋅Y(s) - s⋅y
y/dt
} = s
2
⋅Y(s) – s⋅y
Isolates right-hand side of last expression
Obtains the inverse Laplace transform
-1
{F(s)} + b⋅L
2
2
+1)+y
/(s
+1)) + e
1
2
-1
2
⋅L
+1)}+ y
{1/(s
+1)}+ L
1
– y
, where y
o
1
–3s
– y
+ Y(s) = e
o
1
-1
{G(s)},
–3s
2
/(s
+1)) } =
-1
–3s
2
{e
/(s
+1))},
Page 16-21
= h(0)
o
. Use