Problem type: Differential Equations: Nonhomogeneous Equations and Undetermined

Question

Problem type: Differential Equations: Nonhomogeneous Equations and Undetermined Coeffiecients: Initial Value Problem.
The pictures provided include a trial solution table of families for particular equations and a textbook solution for a specific differential equation problem(initial value problem).
Question: Why wasn't #8 on the trial solution table used? Please explain why the solution used the family for Yp that it did.
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1. Based on #8: Yp=x[ A + (B + Cx)(e^x)] vs. 2.Textbook Solution:Yp=x [ A + (Bx + Cx^2)(e^x)]
----------------------------------—------------------ 1.Trial Solution Table: ------------------------------------------------------- 2. Textbook Solution: TABLE 4.1 Trial Particular Solutions g(x) Form of y, 1. 1 (any constant) A 2, 5x 7 Ax B 3. 3x2 2 Ax2 Bx C 4. x x 1 Ax3 Bx2 Cx E 5. sin 4x A cos 4 x B sin 4x 6. cos 4x A cos 4x B sin 4x 7. e5x 8. (9x 2)e (Ax B) 9. x2e (Ax Bx C) 10, e sin 4x Ae cos 4x Besok sin 4x (Ax2 Bx C cos 4x (Ex2 Fx G) sin 4x 11. 5x2 sin 4x (Aux B)ear cos 4x (Cx E)e" sin 4x 12. xe cos 4x EXAMPLE 5 Forms of Particular Solutions-Case i Determine the form of a particular solution of (a) v 8 25v

Explanation / Answer

function=e^5x(9x-2)

yp(x)=(Ax+B)e^5x

yp'(x)=5(9x2)e^5x+9e^5x

yp''(x)=25(9x2)e^5x+90e^5x

yp'''(x)=125(9x2)e^5x+675e^5x

......and so on

It never stops or converts into any of the other trail solutions to be reduced

****Thank you

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