HP 48gII Uživatelský manuál stáhnout pdf (Strana 148)

Page 14-2

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 examples below are shown in the RPN

mode:

Example 1

– To solve the homogeneous ODE

y/dx

-4

⋅

y/dx

)-11

⋅

(dy/dx)+30

⋅

y = 0.

Enter:

 ` 'XXX' ` DE

The solution is (figure put together from EQW screenshots):

where cC0, cC1, and cC2 are constants of integration. This result can be re-

written as

y = K

⋅e

–3x

+ K

⋅e

+ K

⋅e

Example 2

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

y/dx

-4⋅(d

y/dx

)-11⋅(dy/dx)+30⋅y = x

Enter:

1 2 ... 143 144 145 146 147 148 149 150 151 152 153 ... 174 175

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HP 48gII Uživatelský manuál Strana 148