- #1
flyingpig
- 2,579
- 1
Homework Statement
Solve for general solution with variation of parameter
[tex]y'''(x) - y'(x) = x[/tex]
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??