Hp 50g Graphing Calculator Manual do Utilizador descarregar pdf (Página 482)

100

101

Page 16-5

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 μ.

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

of constants result from factoring out the exponential terms after the Laplace

transform solution is obtained.

Example 2

– Using the function LDEC, solve the non-homogeneous ODE:

y/dx

-4⋅(d

y/dx

)-11⋅(dy/dx)+30⋅y = x

Enter:

'X^2' ` 'X^3-4*X^2-11*X+30' ` LDEC μ

1 2 ... 477 478 479 480 481 482 483 484 485 486 487 ... 886 887

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Hp 50g Graphing Calculator Manual do Utilizador Página 482

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