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

d3y/dx3-4⋅(d2y/dx2)-11⋅(dy/dx)+30⋅y = 0.

Enter:

` 'X X X ' ` DE

The solution is (figure put together from EQW screenshots):

where cC0, cC1, and cC2 are constants of integration. This result can be rewritten as

y = K1⋅e–3x+ K2⋅e5x + K3⋅e2x.

Example 2 – Using the function LDEC, solve the non-homogeneous ODE:

d3y/dx3-4⋅(d2y/dx2)-11⋅(dy/dx)+30⋅y = x2.

Enter:

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