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Power Series Solutions of X of the D.E. and E.A. of the Initial Value

FIND POWER SERIES SOLUTIONS IN POWERS OF X OF THE D.E.
y''-xy'+(3x-2)y=0

and

FIND POWER SERIES SOLUTION OF EA. OF THE INITIAL-VALUE.
y''+xy'-2y=0, y(0)=0, y'(0)=1

ON BOTH OF THE PROBLEMS I GOT STUCK ON THE RECURRENCE FORMULA AND GETTING POWERS OF X.

Solution Summary

The solution includes completed equations and and explanation of the equation process in the attached file.

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