Qcm acm, Cieq – HP 48g Graphing Calculator User Manual
Page 238
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Plotting a Phase Plane for a Vector-Valued Solution
The HP 48 also lets you plot vector-valued equations and select which
vector value is plotted on which axis. As described earlier, another
way to write the second-order equation
y” = ai(i)i/' + ao(t)i/ + 5'(t)
Where w is
fw is
fw * w + c * g(t)
, and c is
0 1
ao(t) ai[t)
The initial condition y'{to) ~
D o
and y{to) = yi can be written w''(to)
= [ yo yi
Example:
19
This is a vector-valued initial condition.
Plot the following equation for tc(l) given that ?/(()) = 0
and ?/'(0) = 0 ( w ( 0 ) = [ 0 0 ] ) :
y" = W + Jyy + .5f + 1
where y(0) = 0 and y'(0) = 0 (dy(0) = [00 ]),
Step 1:
Convert the equation into a first-order equation.
0
1
.5 .5
.5i -|- 1)
Step 2:
Store the values in
fiu
and c.
Qcm acm
0
ciEQ
1
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© [STO) QQD 0 [ S P C l 1
[
enter
)
Q @ C
CEoD
19-12 Differential Equations