HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 483)

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101

Page 16-5

Function LDEC

The calculator provides function LDEC (Linear Differential Equation Command)

to find the general solution to a linear ODE of any order with constant

coefficients, whether it is homogeneous or not. This function requires you to

provide two pieces of input:

• the right-hand side of the ODE

• the characteristic equation of the ODE

Both of these inputs must be given in terms of the default independent variable

for the calculator’s CAS (typically ‘X’). The output from the function is the

general solution of the ODE. The function LDEC is available through in the

CALC/DIFF menu. The examples are shown in the RPN mode, however,

translating them to the ALG mode is straightforward.

Example 1

– To solve the homogeneous ODE: d

y/dx

-4⋅(d

y/dx

11⋅(dy/dx)+30⋅y = 0, enter: 0 ` 'X^3-4*X^2-11*X+30' `

LDEC. The solution is:

where cC0, cC1, and cC2 are constants of integration. While this result

seems very complicated, it can be simplified if we take

K1 = (10*cC0-(7+cC1-cC2))/40, K2 = -(6*cC0-(cC1+cC2))/24,

and

K3 = (15*cC0+(2*cC1-cC2))/15.

Then, the solution is

y = K

⋅e

–3x

+ K

⋅e

+ K

⋅e

The reason why the result provided by LDEC shows such complicated

combination of constants is because, internally, to produce the solution, LDEC

utilizes Laplace transforms (to be presented later in this chapter), which

transform the solution of an ODE into an algebraic solution. The combination

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