A
Vector of coefficients of the different derivatives of a function
x(t), starting with the coefficient of the lowest order term. The node assumes the coefficient of the highest order derivative to be equal to
1.
initial values
Vector of the initial values of the variables.
error in
Error conditions that occur before this node runs.
The node responds to this input according to standard error behavior.
Many nodes provide an
error in
input and an
error out
output so that the node can respond to and communicate errors that occur while code is running. The value of
error in
specifies whether an error occurred before the node runs. Most nodes respond to values of
error in
in a standard, predictable way.
error in
does not contain an error

error in
contains an error



If no error occurred before the node runs, the node begins execution normally.
If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as
error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the
error in
value as
error out.

Default:
No error
formula
Symbolic solution of the differential equation.
error out
Error information.
The node produces this output according to standard error behavior.
Many nodes provide an
error in
input and an
error out
output so that the node can respond to and communicate errors that occur while code is running. The value of
error in
specifies whether an error occurred before the node runs. Most nodes respond to values of
error in
in a standard, predictable way.
error in
does not contain an error

error in
contains an error



If no error occurred before the node runs, the node begins execution normally.
If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as
error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the
error in
value as
error out.

Algorithm for Solving an NOrder Linear Differential Equation
Consider the
norder linear homogeneous differential equation:
${x}^{\left(n\right)}+{a}_{n1}{x}^{(n1)}+\dots +{a}_{1}{x}^{\left(1\right)}+{a}_{0}x=0$
with the following initial conditions:
$x\left(0\right)={x}_{00}\phantom{\rule{0ex}{0ex}}{x}^{\left(1\right)}\left(0\right)={x}_{10}\phantom{\rule{0ex}{0ex}}\vdots \phantom{\rule{0ex}{0ex}}{x}^{(n1)}\left(0\right)={x}_{(n1)0}$
where

a
is the constant coefficient of the differential equation

n
is the highest order of the differential equation

0
is the start time of the ODE solver.
x
_{00}
represents the value of
x(t) when
t=0.
x
_{(n1)0}
represents the (n1)^{th}
derivative of
x(t) when
t
= 0.
To solve the differential equation, let
$x={e}^{\lambda t}$, leading to:
${\lambda}^{n}+{a}_{n1}{\lambda}^{n1}+\dots +{a}_{1}\lambda +{a}_{0}=0$
The
n
zeros of the above equation determine the structure of the solution of the ODE. If we have
n
distinct complex zeros
${\lambda}_{1},\dots {,\lambda}_{n}$, the general solution of the
norder differential equation can be expressed by
$x\left(t\right)={\beta}_{1}{e}^{{\lambda}_{1}t}+\dots +{\beta}_{n}{e}^{{\lambda}_{n}t}$
where
${\beta}_{1},\dots ,{\beta}_{n}$
are arbitrary constants and can be determined by the initial condition (t
= 0).
When
t
= 0,
$x\left(0\right)={\beta}_{1}+\dots +{\beta}_{n}\phantom{\rule{0ex}{0ex}}{x}^{\left(1\right)}\left(0\right)={\beta}_{1}{\lambda}_{1}+\dots +{\beta}_{n}{\lambda}_{n}\phantom{\rule{0ex}{0ex}}\vdots \phantom{\rule{0ex}{0ex}}{x}^{(n1)}\left(0\right)={\beta}_{1}{{\lambda}_{1}}^{n1}+\dots +{\beta}_{n}{{\lambda}_{n}}^{n1}$
Note
If
${\lambda}_{1},\dots {,\lambda}_{n}$
are repeated eigenvalues, this node returns an error code of
23017.
To solve the differential equation
x''  3x' + 2x
= 0 with the initial conditions of
x(0) = 2 and
x'(0) = 3, enter
A
=
[2, 3]
and
initial values
=
[2, 3].
Where This Node Can Run:
Desktop OS: Windows
FPGA:
Not supported
Web Server: Not supported in VIs that run in a web application