Question

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

Exponential models
ANSWERED
asked 2021-06-13

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

Expert Answers (1)

2021-06-14

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

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