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

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

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

aprovard
Answered 2021-06-05 Author has 10947 answers
Starting system is
\(\displaystyle{x}{'''}+{t}{x}{''}+{2}{t}^{{{3}}}{x}'-{5}{t}^{{{4}}}={0}\)
We continue as in example from the book
\(\displaystyle{x}'_{{3}}={x}{'''}\)
\(\displaystyle{x}'_{{2}}={x}{''}\)
\(\displaystyle{x}_{{1}}={x}'\)
\(\displaystyle{x}'_{{1}}={x}_{{2}}\)
\(\displaystyle{x}'_{{2}}={x}_{{3}}\)
\(\displaystyle{x}'_{{3}}=-{2}{t}^{{{3}}}{x}_{{2}}-{t}{x}_{{3}}+{5}{t}^{{{4}}}\)
Have a similar question?
Ask An Expert
46
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-07-05
Transform the second-order differential equation \(\displaystyle{\frac{{{d}^{{{2}}}{x}}}{{{d}{t}^{{{2}}}}}}={3}{x}\) into a system of first-order differential equations.
asked 2021-05-01
Transform the given differential equation or system into an equivalent system of first-order differential equations.
\(\displaystyle{x}^{{{\left({3}\right)}}}={\left({x}'\right)}^{{{2}}}+{\cos{{x}}}\)
asked 2021-06-05
Transform the second-order differential equation \(\displaystyle{\frac{{{d}^{{{2}}}{x}}}{{{d}{t}^{{{2}}}}}}+{\frac{{{d}{x}}}{{{d}{t}}}}={x}\) into a system of first-order differential equations.
asked 2021-06-13

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

asked 2021-05-26
Transform the given differential equation or system into an equivalent system of first-order differential equations.
\(\displaystyle{x}^{{{\left({4}\right)}}}+{3}{x}{''}+{x}={e}^{{{t}}}{\sin{{2}}}{t}\)
asked 2021-06-09

Transform the given differential equation or system into an equivalent system of first-order differential equations.
\(\displaystyle{t}^{{{3}}}{x}^{{{\left({3}\right)}}}-{2}{t}^{{{2}}}{x}{''}+{3}{t}{x}'+{5}{x}={\ln{{t}}}\)

asked 2021-05-05

Transform the given differential equation or system into an equivalent system of first-order differential equations.
\(\displaystyle{x}''+{3}{x}'-{7}{x}={t}^{{{2}}}\)

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question
...