Inexact Differential Equation with 4 Degree

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jeffer vitola
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hello ... I wanted to demonstrate the solution of a differential equation, and as I do not yet know the latex language, then I take pictures of the leaves with my solutions ... the user who wants to give more solutions is well received and is welcome ...
att
jefferson alexander vitola (Smile)
https://www.physicsforums.com/attachments/1063._xfImport
https://www.physicsforums.com/attachments/1064._xfImport
att
jefferson alexander vitola (Smile)

Comments and questions should be posted here:

http://www.mathhelpboards.com/f53/commentary-inexact-differential-equation-4-degree-5704/
 
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  • Handwritten solution of the fourth-order ODE d4y/dx4 - 5 d2y/dx2 + 4y = e^-x, with initial conditions, auxiliary equation m^4 - 5m^2 + 4 = 0, and general solution y_c = C1 e^2x + C2 e^-2x + C3 e^x + C4 e^-x.
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  • Handwritten derivation solving a fourth-order linear ODE by series-style initial conditions, with boxed results: C1 = 1/36, C2 = 1/12, C3 = -61/36, C4 = 11/12, and final solution y = (1/36)e^{2x} + (1/12)e^{-2x} - (61/36)e^{-x} + (11/12)e^{x} + (5/3)e^{-x}... + (1/6)xe^{-x}.
    182.jpg
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Looks correct to me...but a question though to the forum ...in trying to solve for the particular solution, would it be ok setting ##y_p=c_5e^{-x}## rather than ##y_p=c_5e^{-x}+c_6xe^{-x}##? unless i am missing something here...