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If the series y(x) = cx is a solution of the differential equation 1y 5xy + 2y = 0, then Cn+2 = - n=0

If the series y(x) = cnx 

If the series y(x) = cx" is a solution of the differential equation 1y 5xy + 2y = 0, then Cn+2 = - n=0 Cn, n = 1,2,... A general solution of the same equation can be written as y(x) = CY (x) + CY(x), where y (x) = 1 + 2 anx", n=2 Calculate a = a3 = a4 = b = b3 = || b4 = " y (x) = = x + -bnx", n=2 Cn-1+

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Answer To find the values of a2 a3 ad b2 b3 and b4 we need to compare the given series solution yx with the general solution yx c0 y1x c1 y2x and match the coefficients of like powers of x First lets ... blur-text-image

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