# Laplace Transforms; Laplace Transform And Inverses In The Calculator - HP 50g User Manual

Graphing calculator.

'd1y(0) = -0.5'.
solution.
NOTE : To obtain fractional expressions for decimal values use function
Q (See Chapter 5).
Press µµ to simplify the result. Use ˜ @EDIT to see this result:
i.e.,
'y(t) = -((19* 5*SIN( 5*t)-(148*COS( 5*t)+80*COS(t/2)))/190)'.
Press ``J@ODETY to get the string " Linear w/ cst coeff " for
the ODE type in this case.

## Laplace Transforms

The Laplace transform of a function f(t) produces a function F(s) in the
image domain that can be utilized to find the solution of a linear
differential equation involving f(t) through algebraic methods. The steps
involved in this application are three:
1. Use of the Laplace transform converts the linear ODE involving f(t) into
an algebraic equation.
2. The unknown F(s) is solved for in the image domain through algebraic
manipulation.
3. An inverse Laplace transform is used to convert the image function
found in step 2 into the solution to the differential equation f(t).

### Laplace transform and inverses in the calculator

The calculator provides the functions LAP and ILAP to calculate the Laplace
transform and the inverse Laplace transform, respectively, of a function
f(VX), where VX is the CAS default independent variable (typically X). The
calculator returns the transform or inverse transform as a function of X. The
functions LAP and ILAP are available under the CALC/DIFF menu. The
examples are worked out in the RPN mode, but translating them to ALG
mode is straightforward.
Example 1 – You can get the definition of the Laplace transform use the
following: ' f(X) ' `LAP in RPN mode, or LAP(F(X)) in ALG mode.
The calculator returns the result (RPN, left; ALG, right):
Changing to these Exact expressions facilitates the
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