Graphical solution of first-order ode, Graphical solution of first-order ode ,16-59 – HP 50g Graphing Calculator User Manual

Page 536

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Page 16-59

@@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

2

), with x = 0 at t = 0. We know there is no

closed-form expression for the integral, however, we know that the definition of
v(t) is dx/dt = exp(-t

2

).

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) =
f(t, x) = exp(-t

2

). Let's plot the solution, x(t), for t = 0 to 5, by using the following

keystroke sequence:

t

v

0.00

4.000

0.25

3.285

0.50

2.640

0.75

2.066

1.00

1.562

1.25

1.129

1.50

0.766

1.75

0.473

2.00

0.250

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