(Solved): Find two power series solutions of the given differential equation about the ordinary point x = 0. ...

Find two power series solutions of the given differential equation about the ordinary point x = 0. y" 5xy' + y = 0 3x8 8 Y1 = 1 ? ?1 Y1 = 1 ??1 = 1 + Oy? = 1 = 1 + x4 2 x² 2 N?N N|X x² x² 2 - + + 3x4 8 11x4 24 3x4 11x4 24 19x12 80 19x6 80 + 77x6 240 19x6 80 + 77x6 240 and + and Y2 and +... Y2 = x + and and = x + x³ + 2x5 7x? + 3 15 Y? = x + Y2 = x + 4x5 5 2x3 3 2x3 + + Y? = x + x³ + + 7x5 15 4x5 5 + 52x7 105 + 4x13 15 + 7x5 4x7 + 15 15 + 4x> 15 52x7 105 + + + +