HP 50G User Manual

Page 16-20
Example 3 – Consider the equation
d
2
y/dt
2
+y = δ(t-3),
where δ(t) is Dirac’s delta function.
Using Laplace transforms, we can write:
L{d
2
y/dt
2
+y} = L{δ(t-3)},
L{d
2
y/dt
2
} + L{y(t)} = L{δ(t-3)}.
With ‘
Delta(X-3)’ ` LAP , the calculator produces EXP(-3*X), i.e., L{δ(t-3)}
= e
–3s
. With Y(s) = L{y(t)}, and L{d
2
y/dt
2
} = s
2
⋅Y(s) - s⋅y
o
– y
1
, where y
o
= h(0)
and y
1
= h’(0), the transformed equation is s
2
⋅Y(s) – s⋅y
o
– y
1
+ Y(s) = e
–3s
. Use
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:
OBJ ƒ ƒ Isolates right-hand side of last expression
ILAP μ Obtains the inverse Laplace transform
The result is ‘y1*SIN(X)+y0*COS(X)+SIN(X-3)*Heaviside(X-3)’.
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.

HP 50G Specifications

General

Digits	33 digits
Battery type	CR2032
Type	Scientific
Form factor	Pocket

Weight and Dimensions

Weight	220 g
Dimensions (WxDxH)	87 x 184 x 23.5 mm