hp40g+.book Page 34 Friday, December 9, 2005 1:03 AM

 

To produce the solutions for y(0) = 1, type:

 

SUBST(Y(X) =

 

cC0 ⋅ COS(X) + X---------------+ 2 ⋅ cC1 ⋅ SIN(X), cC0 = 1 )

 

2

 

which gives:

 

y(x) = 2---------------------------------------------------------------------------------⋅ cos(x) + (x + 2 ⋅ cC1) ⋅ sin(x)

 

2

 

Example 2

 

Solve:

 

y” + y = cos(x)

 

y(0) = 1 y’(0) = 1

 

It is possible to solve for the constants from the outset.

 

Typing:

 

DESOLVE((d1d1Y(X)+Y(X)=COS(X))

 

AND (Y(0)=1) AND (d1Y(0)=1),Y(X))

 

gives:

 

Y(x) = cosx + 2-----------+x ⋅ sin(x)

 

2

ISOLATE

The zeros of an expression

 

ISOLATE returns the values that are the zeros of an

 

expression or an equation.

 

ISOLATE has two parameters: an expression or equation,

 

and the name of the variable to isolate (ignoring

 

REALASSUME).

 

Typing:

 

ISOLATE(X4-1=3,X)

 

gives in real mode:

 

(x = √2) OR (x = −√2)

 

and in complex mode:

 

(x = √2 · i) OR (x = −√2) OR

 

(x = −(√2 · i)) OR (x = √2)

14-34

 

 

Computer Algebra System (CAS)