Solves an nth-order, homogeneous linear differential equation with constant coefficients in symbolic form.


icon

Inputs/Outputs

  • c1ddbl.png A (a0,a1,...an-1) —

    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.

  • c1ddbl.png X0 —

    X0 is the vector of the start condition x[10], …, x[n0].

    There is a one-to-one relation between the components of X0 and X.

  • istr.png formula —

    formula is the symbolic solution.

  • ii32.png error —

    error returns any error or warning from the VI. Errors are produced by using the wrong inputs X, X0, and F(X,t). You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

    • The general solution has the following form.

    x(t) = β1exp(λ1t) + … + βnexp(λnt)

    with complex

    β1, …, βn

    and

    λ1, …, λn

    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 λ1, …, λn 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].

    Refer to the ODE Linear nth Order Numeric VI for more information about nth-order, homogeneous linear differential equations.