(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Solve for general solution with variation of parameter

[tex]y'''(x) - y'(x) = x[/tex]

3. The attempt at a solution

I initially looked at [tex]y'''(x) - y'(x) = x[/tex] only and I foudn my answer to be

[tex]y(x) = C_1e^{x} + C_2e^{-x} + 1 - x[/tex]

Now i looked through my book and it says it works for ay'' + by' + c = f(t) only (second order).

So I "integrated" [tex]y'''(x) - y'(x) = x[/tex]

And I got [tex]y''(x) - y(x) = \frac{x^2}{2} + C[/tex], solving I got

[tex]y(x) = C_1e^{x} + C_2e^{-x} + C_3 - \frac{x^2}{2}[/tex]

Using the computer, it gave me

http://www.wolframalpha.com/input/?i=Solve[y%27%27%27+-+y%27+%3D+x]

Why does computer have negative sign??

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# Variation of parameters

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