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Function LDEC
The calculator provides function LDEC (Linear Differential Equation Command)
to find the general solution to a linear ODE of any order with constant
coefficients, whether it is homogeneous or not. This function requires you to
provide two pieces of input:
• 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
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