Method of Undetermined Coefficients - Nonhomogeneous 2nd Order Differential Equations

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"Modification Rule: If a term in your choice for (Yp) happens to be a solution of the homogeneous ODE corresponding to y''+ay'+by=r(x), multiply this term by x (or by x^2 if this solution corresponds to a double root of the characteristic equation of the homogeneous ODE)." ERWIN KREYSZIG - ADVANCED ENGINEERING MATHEMATICS - P81

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[@71499lion]

so basically if a solution to the left side is say 3 and 3 appears as one of the constants Yp you solve for then that term needs to be multiplied by x? assuming it wasn't (x-3)^2=0 in which case you'd multiply that term in Yp by x^2

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But what allows us to multiply x just like that?

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happened to me today it was for xe^x which is a a first degree equation the Solution ended up being in the third degree

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Small error in 16:35, the derivative of -sin =/= cos. It should be d/dx (-sin) == -cos.

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Professor Organic Chemistry Tutor, thank you for an excellent video/lecture on The Method of Undetermined Coefficients in Calculus Three/ Introductory Differential Equations. The solutions to Nonhomogeneous 2nd Order Differential Equations are not difficult to solve but messy from start to finish. Once again, the great viewers have found and corrected the error/ errors in this video.

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3:42 I believe its a first case 2nd ode, since 2nd case uses 1 root and C2 * X * e^(rx)

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