HP 49g+ - The Variable ODETYPE

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The variable ODETYPE
You will notice in the soft-menu key labels a new variable called @ODETY
(ODETYPE). This variable is produced with the call to the DESOL function and
holds a string showing the type of ODE used as input for DESOLVE. Press
@ODETY to obtain the string “1st order linear”.
Example 2
– Solving an equation with initial conditions. Solve
d
2
y/dt
2
+ 5y = 2 cos(t/2),
with initial conditions
y(0) = 1.2, y’(0) = -0.5.
In the calculator, use:
[‘d1d1y(t)+5*y(t) = 2*COS(t/2)’ ‘y(0) = 6/5’ ‘d1y(0) = -1/2’]
`
‘y(t)’
`
DESOLVE
Notice that the initial conditions were changed to their
Exact expressions,
‘y(0) = 6/5’, rather than ‘y(0)=1.2’, and ‘d1y(0) = -1/2’, rather than, ‘d1y(0)
= -0.5’. Changing to these Exact expressions facilitates the solution.
Note: To obtain fractional expressions for decimal values use function
 Q
(See Chapter 5).
Press
µµ to simplify the result. The solution is:
i.e.,
‘y(t) = -((19*5*SIN(√5*t)-(148*COS(√5*t)+80*COS(t/2)))/190)’.
Press
J @ODETY to get the string “Linear w/ cst coeff” for the ODE type
in this case.