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14-34 Computer Algebra System (CAS)
To produce the solutions for y(0) = 1, type:
which gives:
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:
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(X
4
-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)
S
UBST Y X()(
c
C0 COS X()⋅
X2+cC1⋅
2
----------------+ SIN X()cC0,⋅ 1 )
=
=
yx()
2 x()cos⋅ x 2+ cC1⋅()+ x()sin⋅
2
----------------------------------------------------------------------------------
=
Yx() xcos
2 x+
2
------------
+ x()sin⋅=
hp40g+.book Page 34 Friday, December 9, 2005 1:03 AM