Define system of simultaneous ordinary differential equations?

Question
Equations
Define system of simultaneous ordinary differential equations?

2020-12-01
Step 1
For First order:
On simultaneous ordinary differential equation of the first order in which there are one or more than one variable in the number of equations.
Examples:
y'=y+2x
$$\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}={3}{y}+{2}{x}$$
Step 2
For Second order:
The simultaneous ordinary differential equations of the second order has one or more than one variable in the number of equations.
Examples:
$$\displaystyle{y}{''}+{4}{y}'+{4}{y}={25}{x}+{16}{e}^{{t}}$$
$$\displaystyle\frac{{{d}^{{2}}{y}}}{{{\left.{d}{x}\right.}^{{2}}}}+\frac{{5}}{{2}}\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}+{9}{y}={88}{x}+{5}{e}^{{t}}$$

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