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

y'' + 3y' + 2y = sin(e^x)

2. Relevant equations

3. The attempt at a solution

[tex] y'' + 3y' + 2y = sin(e^x) [/tex]

[tex] m^2 + 3m + 2 = 0[/tex]

[tex] m1 = -2 ; m2 = -1[/tex]

[tex] yc = c1e^{-2x} c2 e^{-x}[/tex]

[tex] y1 = e^{-2x}[/tex]

[tex] y1' = -2e^{-2x}[/tex]

[tex] y2 = e^{-x}[/tex]

[tex] y2' = -e^{-x}[/tex]

The W Matrix works out to

[tex] W = e^{-3x}[/tex]

[tex] u1' = -e^{x}sin(e^x)[/tex]

[tex] u1 = sin(e^x)[/tex]

[tex] u2' = e^{2x}sin(e^x)[/tex]

[tex] u2 = -e^xcos(e^x) + sin(e^x)[/tex]

(This is the integration by parts solution in an earlier posting:

https://www.physicsforums.com/showthread.php?t=207521

my solution:

[tex] y = c1e^{-2x} + c2e^{-x} + e^{-2x}sin(e^x) + e^{-x}[-e^xcos(e^x) + sin(e^x)][/tex]

The book's solution:

[tex] y = c1e^{-2x} + c2e^{-x} - e^{-2x}sin(e^x) [/tex]

(I'm not in school but this is a problem out of a book - I'm trying to brush up)

Thanks for the help

-Sparky

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# Homework Help: A differential Equation -

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