Question: Use power series to solve the initial value problem. y' + zy = 0, y(0) = 6, y (0) = 0 hint: after shifting indices,

Use power series to solve the initial value problem. y' + zy = 0, y(0) = 6, y (0) = 0 hint: after shifting indices, expand each series term-by-term rather than seeking a recurrence relation. y(z) = (-1) An (An - 1) (47 - 4) (47 - 5) ...4 . 3 -4n O y(z) = Z (-1) An(4n - 1) (47 - 4) (471 - 5) . . . 4 - 3 in y(z) = -6+ 2(-1) An (4n - 1) (47 - 4) (47 - 5) .. .4 . 3 y(z) = 6+ 2 (-1) In (An -1) (4n - 4) (4n - 5) .. .4. 3 1 1 y(z) - Z(-1) An (4n - 1) (471 - 4) (4n - 5). . .4 . 3

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