hp40g+.book Page 35 Friday, December 9, 2005 1:03 AM

LDEC

Linear differential equations having constant

 

 

coefficients

 

 

 

 

 

LDEC enables you to directly solve linear differential

 

equations having constant coefficients.

 

 

 

The parameters are the second member and the

 

 

characteristic equation.

 

 

 

 

Solve:

 

 

 

 

 

y” − 6 · y’ + 9 · y = x · e3·x

 

 

 

 

Typing:

 

 

 

 

 

LDEC(X·EXP(3·X),X2−6·X+9)

 

 

 

gives:

 

 

 

 

 

⎛(18 ⋅ x – 6) ⋅ cC0 – (6 ⋅ x ⋅ cC1

+ x3)

 

⎞

 

-⎝----------------------------------------------------------------------------------------

6

 

⋅ exp(3

⋅ x)⎠

 

cC0 and cC1 are integration constants (y(0) = cC0 and

 

y’(0) = cC1).

 

 

 

 

LINSOLVE

Solve linear system

 

LINSOLVE enables you to solve a system of linear

 

equations.

 

It is assumed that the various equations are of the form

 

expression = 0.

 

LINSOLVE has two arguments: the first members of the

 

various equations separated by AND, and the names of

 

the various variables separated by AND.

 

Example 1

 

Typing:

 

LINSOLVE(X+Y+3 AND X-Y+1, X AND Y)

 

gives:

 

(x = −2) AND (y = −1)

 

or, in Step-by-step mode (CFG, etc.):

 

L2=L2−L1

1 1 3

1–1 1

ENTER

Computer Algebra System (CAS)

14-35