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)
= 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:
Change the independent variable to t .
Accept changes to PLOT SETUP: L @@OK@@
„ò (simultaneously, if in RPN mode). To enter PLOT WINDOW
Change the horizontal and vertical view window to the following settings:
), with x = 0 at t = 0. We know there is no