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
ANSWERED
asked 2021-06-04
Transform the single linear differential equation into a system of first-order differential equations.
\(\displaystyle{x}{'''}+{t}{x}{''}+{2}{t}^{{{3}}}{x}'-{5}{t}^{{{4}}}={0}\)

Answers (1)

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
\(\displaystyle{x}'_{{3}}={x}{'''}\)
\(\displaystyle{x}'_{{2}}={x}{''}\)
\(\displaystyle{x}_{{1}}={x}'\)
\(\displaystyle{x}'_{{1}}={x}_{{2}}\)
\(\displaystyle{x}'_{{2}}={x}_{{3}}\)
\(\displaystyle{x}'_{{3}}=-{2}{t}^{{{3}}}{x}_{{2}}-{t}{x}_{{3}}+{5}{t}^{{{4}}}\)
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