Note that x = 0 is an ordinary point of the differential
Chapter , Problem 21RP(choose chapter or problem)
Note that x = 0 is an ordinary point of the differential equation \(y^{\prime \prime}+x^{2} y^{\prime}+2 x y=5-2 x+10 x^{3}\). Use the assumption \(y=\sum_{n=0}^{\infty} c_{n} x^{n}\) to find the general solution \(y=y_{c}+y_{p}\) that consists of three power series centered at x = 0.
Text Transcription:
y^prime\prime+x^2y^prime+2xy=5-2x+10x^3
y=sum_n=0^inftyc_nx^n
y=y_c+y_p
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