HP 48gII Note, @ODET, @ODET, J @ODET, The variable ODETYPE

The variable ODETYPE

You will notice in the soft-menu key labels a new variable called @ODET (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 @ODET to obtain the string “1st order linear”.

Example 2 – Solving an equation with initial conditions. Solve

d2y/dt2 + 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 ÆQ (See Chapter 5).

Press µµto 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 @ODET to get the string “Linear w/ cst coeff” for the ODE type in this case.

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