I just need a hint or something to see where I start. I'm at a loss for a beginning.(adsbygoogle = window.adsbygoogle || []).push({});

Consider the non-homogenous equation

[tex]y'' + xy' + y = x^2 +2x +1[/tex]

Find the power series solution about [tex]x=0[/tex] of the equation and express your answer in the form:

[tex]y=a_0 y_1 + a_1 y_2 + y_p[/tex]

where [tex]a_0[/tex] and [tex]a_1[/tex] are arbitrary constants. Give only the first three nonzero terms of each of the three series[tex]y_1[/tex],[tex]y_2[/tex], and [tex]y_p[/tex]

Hint: Substitute [tex] y = \sum_{n=0}^{\infty}a_nx^{n}[/tex] and equate coefficients to find [tex]a_n[/tex], [tex]n = 2,3,4,5[/tex]

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# Homework Help: Non-homogeneous 2nd order diff eq involves power series

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