- #1

- 11

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[tex]x''(t) + 3 x'(t) + 2x(t) = 0, x(0) = 2, x'(0) = -2[/tex]

My Steps:

-Convert everything into its Laplace Transform

[tex](s^2X - sx(0) - x'(0)) + 3(s'X - x(0)) + /2X) = 0[/tex]

-Replace with initial values

[tex](s^2X - 2s - (-2) ) + 3(s'X - 2) + 2X) = 0[/tex]

-Distribute

[tex]s^2X - 2s + 2 + 3s'X - 6 + 2X = 0[/tex]

-Add like terms

[tex]s^2X - 2s + 3s'X +2X - 4 = 0[/tex]

-Group the s terms, then simplify

[tex]X(s^2 - 3s' + 2) - 2s - 4 = 0[/tex]

-Isolate [tex]X[/tex]

[tex]X = \frac{2s + 4}{s^2 - 3s' + 2}[/tex]

Now I'm not sure if I'm done since I missed one lecture. I'd appreciate it if someone could check over and point over/highlight any errors I made. Please and thank you!