ODE Linear nth Order Symbolic (Not in Base Package)

Solve an nth order homogeneous linear differential equation with constant coefficients in symbolic form. Details

A is the vector of coefficients of the different derivatives of a function x(t), starting with the coefficient of the lowest order term. The coefficient of the highest order derivative is assumed to be equal to 1.0 and does not need to be entered.
X0 is the vector of the start condition . There is a one-to-one relation between the components of X0 and X.
formula is the symbolic solution.
errors are produced by using the wrong inputs X, X0, and F(X,t).

ODE Linear nth Order Symbolic Details

The general solution has the following form. Refer to the ODE Linear nth Order Numeric VI for more information.

with complex

and

But all inputs are real, and thus the solution also has this property. As a consequence, the symbolic solution is a linear combination of exp, sin-, and cos-functions with real coefficients.

Note  Only the case of pairwise different is treated. For the case of repeated eigenvalues, an error code of –23017 is given. By convention, the value of the highest coefficient is taken as 1.0, and does not need to be entered in the A control. The other coefficients are entered starting with the lowest order coefficient.

To solve the differential equation

x'' – 3 x' + 2 x = 0

with the I.C. as with x(0) = 2 and x'(0) = 3

enter A = [2, –3] and X0 = [2, 3]