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We can use this result as the first input to the function LDEC when used to obtain
a solution to the system d
2
y/dX
2
+ 0.25y = SW(X), where SW(X) stands for
Square Wave function of X. The second input item will be the characteristic
equation corresponding to the homogeneous ODE shown above, i.e.,
‘X^2+0.25’ .
With these two inputs, function LDEC produces the following result (decimal
format changed to Fix with 3 decimals).
Pressing ˜ allows you to see the entire expression in the Equation writer.
Exploring the equation in the Equation Writer reveals the existence of two
constants of integration, cC0 and cC1. These values would be calculated using
initial conditions. Suppose that we use the values cC0 = 0.5 and cC1 = -0.5,
we can replace those values in the solution above by using function SUBST (see
Chapter 5). For this case, use SUBST(ANS(1),cC0=0.5) `, followed by
SUBST(ANS(1),cC1=-0.5) `. Back into normal calculator display we can
use:
The latter result can be defined as a function, FW(X), as follows (cutting and
pasting the last result into the command):
We can now plot the real part of this function. Change the decimal mode to
Standard, and use the following: