Desolve; Diagmap - HP 48gII Advanced User's Reference Manual

Input: The function or list of functions to be differentiated.
Output: The derivative, or a vector of the derivatives, of the function or functions.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
See also: DERIV, dn, ∂

DESOLVE

Type: Command
Description: Solves certain first-order ordinary differential equations with respect to the current variable.
Symbolic solve, !Î or calculus, !Ö
Access:
Input: Level 2/Argument 1: A first-order differential equation.
Level 1/Argument 2: The function to solve for.
Output: The solution to the equation, either y as a function of x or x as a function of y, or x and y as
functions of a parameter.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example: Solve the following differential equation:
y x + 2y x
Command:
DESOLVE(d1Y(X)+2*Y(X)=EXP(3*X),Y(X))
(See the description of dn and Chapter 16 of the User's Guide for an explanation of the use of
"d1" for a derivative. )
Result:
{Y(X)=(1/5*EXP(5*X)+cC0)*(1/EXP(X)^2)}
See also: dn, LDEC

DIAGMAP

Type: Command
Description: Applies an holomorphic operator to a diagonalizable matrix.
Matrices, !Ø L
Access:
Input: Level 2/Argument 1: A diagonalizable matrix.
Level 1/Argument 2: An operator, expressed as a function. The function can be stored in a
variable with DEF, or can be a program, or a single expression.
Output: The matrix that results from applying the operator to the matrix.
Flags: Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag –3 clear).
Example: Apply the operator e
DIAGMAP 1 1
Command:
or
DIAGMAP([[1,1],[0,2]],exp(X))
EXP 1
0
Result:
4-22 Computer Algebra Commands
3x
= e
EIGENVECTORS
to the matrix
x
⎛
⎜
<< X<<EXP(X)>> >>
⎝
0 2
– EXP 1 + EXP 2
EXP 2
DIFFERENTIAL EQNS
.
1 1
0 2
⎞
⎟
⎠
.