ODE Linear System Symbolic (Not in Base Package)

Solves an n-dimension linear system of differential equations with a given start condition. The solution is based on the determination of the eigenvalues and eigenvectors of the underlying matrix. The solution is given in symbolic form. Details

A is the n by n matrix describing the linear system.
X0 is the n vector describing the start condition. . There is a one-to-one relation between the components of X0 and X.
formula is a string with the solution of the linear system in the standard formula notation of LabVIEW. The solution vector elements are separated by carriage return.
errors are produced by using the wrong inputs X, X0, and F(X,t).

ODE Linear System Symbolic Details

Note  This VI works properly for almost all cases of real matrices A that can have repeated eigenvalues, conjugate complex eigenvalues, and so on. The exception is the case of a singular eigenvector matrix, that is, a matrix in which the eigenvectors do not span the whole space. An error of -23016 is given if the eigenvector matrix is singular.

The linear differential equation described by the following system:

with

has the solution

+ 1.62*exp(–12.46*t) – 1.28*exp(–6.30*t) + 0.63*exp(1.34*t) + 0.04*exp(5.42*t)

+ 0.84*exp(–12.46*t) – 0.29*exp(–6.30*t) + 1.51*exp(1.34*t) – 0.06*exp(5.42*t)

–0.73*exp(–12.46*t) + 0.01*exp(–6.30*t) + 3.69*exp(1.34*t) + 0.02*exp(5.42*t)

+ 0.87*exp(–12.46*t) + 2.67*exp(–6.30*t) + 0.45*exp(1.34*t) + 0.01*exp(5.42*t)

Enter the equations above on the front panel as follows: