HP 49g+ User Manual page 499

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OBJ
ILAP
The result is 'y1*SIN(X-1)+y0*COS(X-1)-(COS(X-3)-1)*Heaviside(X-3)'.
Thus, we write as the solution: y(t) = y
Check what the solution to the ODE would be if you use the function LDEC:
'H(X-3)' `[ENTER] 'X^2+1' ` LDEC
The result is:
Please notice that the variable X in this expression actually represents the
variable t in the original ODE, and that the variable ttt in this expression is a
dummy variable. Thus, the translation of the solution in paper may be written
as:
) ( cos
y t Co t
Example 4 – Plot the solution to Example 3 using the same values of y
used in the plot of Example 1, above. We now plot the function
y(t) = 0.5 cos t –0.25 sin t + (1+sin(t-3))⋅H(t-3).
In the range 0 < t < 20, and changing the vertical range to (-1,3), the graph
should look like this:
Isolates right-hand side of last expression
Obtains the inverse Laplace transform
cos t + y
o
∞
sin sin (
C t t H u
1
0
sin t + H(t-3)⋅(1+sin(t-3)).
1
− ut
) 3 .
e du
and y
o
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