Question

# Transform the single linear differential equation into a system of first-order differential equations.x''-3x'+2x=t^{2}

Exponential models

Transform the single linear differential equation into a system of first-order differential equations.
$$\displaystyle{x}{''}-{3}{x}'+{2}{x}={t}^{{{2}}}$$

2021-06-14

Starting system is
$$\displaystyle{x}{''}-{3}{x}'+{2}{x}={t}^{{{2}}}$$
We continue as in example from the book
$$\displaystyle{x}'_{{2}}={x}{''}$$
$$\displaystyle{x}'_{{1}}={x}'$$
$$\displaystyle{x}'_{{1}}={x}_{{2}}$$
$$\displaystyle{x}'_{{2}}=-{2}{x}_{{1}}+{3}{x}_{{2}}+{t}^{{{2}}}$$