# HP 48gII User Manual Page 496

Graphing calculator.

Example 1 – To solve the first order equation,
by using Laplace transforms, we can write:
Note: 'EXP(-X)' ` LAP , produces '1/(X+1)', i.e., L{e
With H(s) = L{h(t)}, and L{dh/dt} = s⋅H(s) - h
equation is
Use the calculator to solve for H(s), by writing:
'X*H-h0+k*H=a/(X+1)' ` 'H' ISOL
The result is
'H=((X+1)*h0+a)/(X^2+(k+1)*X+k)'.
To find the solution to the ODE, h(t), we need to use the inverse Laplace
transform, as follows:
ƒ ƒµ
OBJ
ILAP
The result is
and simplifying, results in
Check what the solution to the ODE would be if you use the function LDEC:
'a*EXP(-X)' ` 'X+k' ` LDEC µ
dh/dt + k⋅h(t) = a⋅e
L{dh/dt + k⋅h(t)} = L{a⋅e
L{dh/dt} + k⋅L{h(t)} = a⋅L{e
, where h
o
s⋅H(s)-h
+k⋅H(s) = a/(s+1).
o
Isolates right-hand side of last expression
Obtains the inverse Laplace transform
. Replacing X with t in this expression
h(t) = a/(k-1)⋅e
–t
,
–t
},
–t
}.
–t
}=1/(s+1).
= h(0), the transformed
o
-t
+((k-1)⋅h
-a)/(k-1)⋅e
o
Page 16-18
-kt
.