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Mathematics LibreTexts

Section 10.7 Answers

  • Page ID
    30071
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    1. \(\left[\begin{array}{c}{5e^{4t}+e^{-3t}(2+8t)}\\{-e^{4t}-e^{-3t}(1-4t)}\end{array}\right]\)

    2. \(\left[\begin{array}{c}{13e^{3t}+3e^{-3t}}\\{-e^{3t}-11e^{-3t}}\end{array}\right]\)

    3. \(\frac{1}{9}\left[\begin{array}{c}{7-6t}\\{-11+3t}\end{array}\right]\)

    4. \(\left[\begin{array}{c}{5-3e^{t}}\\{-6+5e^{t}}\end{array}\right]\)

    5. \(\left[\begin{array}{c}{e^{-5t}(3+6t)+e^{-3t}(3-2t)}\\{-e^{-5t}(3+2t)-e^{-3t}(1-2t)}\end{array}\right]\)

    6. \(\left[\begin{array}{c}{t}\\{0}\end{array}\right]\)

    7. \(-\frac{1}{6}\left[\begin{array}{c}{2-6t}\\{7+6t}\\{1-12t}\end{array}\right]\)

    8. \(-\frac{1}{6}\left[\begin{array}{c}{3e^{t}+4}\\{6e^{t}-4}\\{10}\end{array}\right]\)

    9. \(\frac{1}{18}\left[\begin{array}{c}{e^{t}(1+12t)-e^{-5t}(1+6t)}\\{-2e^{t}(1-6t)-e^{-5t}(1-12t)}\\{e^{t}(1+12t)-e^{-5t}(1+6t)}\end{array}\right]\)

    10. \(\frac{1}{3}\left[\begin{array}{c}{2e^{t}}\\{e^{t}}\\{2e^{t}}\end{array}\right]\)

    11. \(\left[\begin{array}{c}{t\sin t}\\{0}\end{array}\right]\)

    12. \(-\left[\begin{array}{c}{t^{2}}\\{2t}\end{array}\right]\)

    13. \((t-1)(\ln |t-1|+t)\left[\begin{array}{c}{1}\\{-1}\end{array}\right]\)

    14. \(\frac{1}{9}\left[\begin{array}{c}{5e^{2t}-e^{-3t}}\\{e^{3t}-5e^{-2t}}\end{array}\right]\)

    15. \(\frac{1}{4t}\left[\begin{array}{c}{2t^{3}\ln |t|+t^{3}(t+2)}\\{2\ln |t|+3t-2}\end{array}\right]\)

    16. \(\frac{1}{2}\left[\begin{array}{c}{te^{-t}(t+2)+(t^{3}-2)}\\{te^{t}(t-2)+(t^{3}+2)}\end{array}\right]\)

    17. \(-\left[\begin{array}{c}{t}\\{t}\\{t}\end{array}\right]\)

    18. \(\frac{1}{4}\left[\begin{array}{c}{-3e^{t}}\\{1}\\{e^{-t}}\end{array}\right]\)

    19. \(\left[\begin{array}{c}{2t^{2}+t}\\{t}\\{-t}\end{array}\right]\)

    20. \(\frac{e^{t}}{4t}\left[\begin{array}{c}{2t+1}\\{2t-1}\\{2t+1}\end{array}\right]\)

    22. 

    1. \({\bf y'}=\left[\begin{array}{cccc}{0}&{1}&{\ldots }&{0}\\{0}&{0}&{\ldots }&{0}\\{\vdots }&{\vdots }&{\ddots }&{\vdots }\\{0}&{0}&{\ldots }&{1}\\{-P_{n}(t)/P_{0}(t)}&{-P_{n-1}/P_{0}(t)}&{\ldots }&{-P_{1}(t)/P_{0}(t)}\end{array}\right]{\bf y}+\left[\begin{array}{c}{0}\\{0}\\{\vdots }\\{F(t)/P_{0}(t)}\end{array}\right]\)
    2. \(\left[\begin{array}{cccc}{y_{1}}&{y_{2}}&{\ldots }&{y_{n}}\\{y'_{1}}&{y'_{2}}&{\ldots }&{y'_{n}}\\{\vdots }&{\vdots }&{\ddots }&{\vdots }\\{y_{1}^{(n-1)}}&{y_{2}^{(n-1)}}&{\ldots }&{y_{n}^{(n-1)}}\end{array}\right]\)