00 If the series y(x) = is a solution of the differential equation 2y - 2xy'...

 

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00 If the series y(x) =" is a solution of the differential equation 2y" - 2x²y' + 1y = 0, then n=0 Cn+2 = (2(n-1))/(2(n+1)(n+2)) Cn 1+ -1/(2(n+1)(n+2)) Cn, n=1,2,... A general solution of the same equation can be written as y(x) = Coy₁ (x) + C₁y₂(x), where Calculate a₂ = a3 = a4= b₂ = b3 = b₁ = y₁(x) = 1 + Y₂(x) = x + 12 1 2 00 If the series y(x) =" is a solution of the differential equation 2y" - 2x²y' + 1y = 0, then n=0 Cn+2 = (2(n-1))/(2(n+1)(n+2)) Cn 1+ -1/(2(n+1)(n+2)) Cn, n=1,2,... A general solution of the same equation can be written as y(x) = Coy₁ (x) + C₁y₂(x), where Calculate a₂ = a3 = a4= b₂ = b3 = b₁ = y₁(x) = 1 + Y₂(x) = x + 12 1 2