The result is:
'SIN(X-3)*Heaviside(X-3) + cC1*SIN(X) + cC0*COS(X)'.
Please notice that the variable X in this expression actually represents the
variable t in the original ODE. Thus, the translation of the solution in paper may
be written as:
When comparing this result with the previous result for y(t), we conclude that
Defining and using Heaviside's step function in the calculator
The previous example provided some experience with the use of Dirac's delta
function as input to a system (i.e., in the right-hand side of the ODE describing
the system). In this example, we want to use Heaviside's step function, H(t). In
the calculator we can define this function as:
This definition will create the variable @@@H@@@ in the calculator's soft menu key.
Example 1 – To see a plot of H(t-2), for example, use a FUNCTION type of
plot (see Chapter 12):
Press „ô, simultaneously in RPN mode, to access to the PLOT SETUP
Change EQ to 'H(X-2)'.
Make sure that
Press L @@@OK@@@ to return to normal calculator display.
Press „ò, simultaneously, to access the PLOT window.
Change the H-VIEW range to 0 to 20, and the V-VIEW range to -2 to 2.
Press @ERASE @DRAW to plot the function .
'H(X) = IFTE(X>0, 1, 0)' `„à
, if needed
is set to 'X'.