HP 50G - Page 145

Page 14-2
• the right-hand side of the ODE
• the characteristic equation of the ODE
Both of these inputs must be given in terms of the default independent
variable for the calculator’s CAS (typically X). The output from the function
is the general solution of the ODE. The examples below are shown in the
RPN mode:
Example 1 – To solve the homogeneous ODE
d
3
y/dx
3
-4⋅(d
2
y/dx
2
)-11⋅(dy/dx)+30⋅y = 0.
Enter:
0 ` 'X^3-4*X^2-11*X+30'` LDEC µ
The solution is (figure put together from EQW screenshots):
where cC0, cC1, and cC2 are constants of integration. This result is
equivalent to
y = K
1
⋅e
–3x
+ K
2
⋅e
5x
+ K
3
⋅e
2x
.
Example 2 – Using the function LDEC, solve the non-homogeneous ODE:
d
3
y/dx
3
-4⋅(d
2
y/dx
2
)-11⋅(dy/dx)+30⋅y = x
2
.
Enter:
'X^2' ` 'X^3-4*X^2-11*X+30'` LDEC µ
The solution is:
which is equivalent to
y = K
1
⋅e
–3x
+ K
2
⋅e
5x
+ K
3
⋅e
2x
+ (450⋅x
2
+330⋅x+241)/13500.
Ch14_DifferentialEquationsQS.fm Page 2 Friday, March 17, 2006 6:23 PM