8. In solving the DE 2x²y"−xy'+(x² +1)y=0 about the ordinary singular point x = 0, it is found that 2r² -3r+1=0 and [(k+r)(2k +2r-3) + 1]ck +Ck-2=0 with co arbitrary and ci=0 (a) Find the indicial root, showing all work. (b) For each indicial root, find the recursive formula and generate three non-zero terms of the series solution. (c) Write the general solution to the DE.

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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8. In solving the DE 2x²y″ −xy'+(x² +1)y=0 about the ordinary singular point x =
0, it is found that 2r² -3r+1=0 and [(k+r)(2k+2r-3)+1]ck + Ck-2=0 with co arbitrary
and ci=0
(a) Find the indicial root, showing all work.
(b) For each indicial root, find the recursive formula and generate three non-zero terms of
the series solution.
(c) Write the general solution to the DE.
Transcribed Image Text:8. In solving the DE 2x²y″ −xy'+(x² +1)y=0 about the ordinary singular point x = 0, it is found that 2r² -3r+1=0 and [(k+r)(2k+2r-3)+1]ck + Ck-2=0 with co arbitrary and ci=0 (a) Find the indicial root, showing all work. (b) For each indicial root, find the recursive formula and generate three non-zero terms of the series solution. (c) Write the general solution to the DE.
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