Graphical Solution Of First-Order Ode - HP 50g User Manual
Graphing calculator
Hide thumbs
Also See for 50g:
- Advanced user's reference manual (693 pages) ,
- User manual (184 pages) ,
- Quick start manual (47 pages)
Table of Contents
Advertisement
@@OK@@ @INIT+—.75 @@OK@@ ™™@SOLVE (wait) @EDIT
(Changes initial value of t to 0.5, and final value of t to 0.75, solve for v(0.75)
= 2.066...)
@@OK@@ @INIT+—1 @@OK@@ ™ ™ @SOLVE (wait) @EDIT
(Changes initial value of t to 0.75, and final value of t to 1, solve for v(1) =
1.562...)
Repeat for t = 1.25, 1.50, 1.75, 2.00. Press @@OK@@ after viewing the last result in
@EDIT. To return to normal calculator display, press $ or L@@OK@@. The
different solutions will be shown in the stack, with the latest result in level 1.
The final results look as follows (rounded to the third decimal):
Graphical solution of first-order ODE
When we can not obtain a closed-form solution for the integral, we can always
plot the integral by selecting Diff Eq in the TYPE field of the PLOT
environment as follows: suppose that we want to plot the position x(t) for a
velocity function v(t) = exp(-t
closed-form expression for the integral, however, we know that the definition of
v(t) is dx/dt = exp(-t
The calculator allows for the plotting of the solution of differential equations of
the form Y'(T) = F(T,Y). For our case, we let Y = x and T = t, therefore, F(T,Y) =
2
f(t, x) = exp(-t
). Let's plot the solution, x(t), for t = 0 to 5, by using the following
keystroke sequence:
t
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2
), with x = 0 at t = 0. We know there is no
2
).
v
4.000
3.285
2.640
2.066
1.562
1.129
0.766
0.473
0.250
Page 16-59
Advertisement
Table of Contents
