Question

# Transform the single linear differential equation into a system of first-order differential equations. x'''+tx''+2t^{3}x'-5t^{4}=0

Differential equations
Transform the single linear differential equation into a system of first-order differential equations.
$$\displaystyle{x}{'''}+{t}{x}{''}+{2}{t}^{{{3}}}{x}'-{5}{t}^{{{4}}}={0}$$

2021-06-05
Starting system is
$$\displaystyle{x}{'''}+{t}{x}{''}+{2}{t}^{{{3}}}{x}'-{5}{t}^{{{4}}}={0}$$
We continue as in example from the book
$$\displaystyle{x}'_{{3}}={x}{'''}$$
$$\displaystyle{x}'_{{2}}={x}{''}$$
$$\displaystyle{x}_{{1}}={x}'$$
$$\displaystyle{x}'_{{1}}={x}_{{2}}$$
$$\displaystyle{x}'_{{2}}={x}_{{3}}$$
$$\displaystyle{x}'_{{3}}=-{2}{t}^{{{3}}}{x}_{{2}}-{t}{x}_{{3}}+{5}{t}^{{{4}}}$$