# Graphical Solution Of First-order Ode - HP 48gII User Manual

Graphing calculator.

## 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
2
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:
„ô (simultaneously, if in RPN mode) to enter PLOT environment
Highlight the field in front of TYPE, using the —˜keys.
@CHOOS, and highlight Diff Eq, using the —˜keys. Press @@OK@@.
Change field F: to 'EXP(- t^2)'
Make sure that the following parameters are set to: H-VAR: 0, V-VAR:
1
Change the independent variable to t .
Accept changes to PLOT SETUP: L @@OK@@
„ò (simultaneously, if in RPN mode). To enter PLOT WINDOW
environment
Change the horizontal and vertical view window to the following settings:
H-VIEW: -1
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
2
), with x = 0 at t = 0. We know there is no
5;
V-VIEW: -1
Then, press
1.5
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