If the series y(x) = cx is a solution of the differential equation 1y 5xy...
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If the series y(x) = Σcx" is a solution of the differential equation 1y” − 5x²y + 2y = 0, then Cn+2 = - n=0 Cn, n = 1,2,... A general solution of the same equation can be written as y(x) = C₁Y₁ (x) + C₁Y₂(x), where ∞ y (x) = 1 + 2 anx", Σ n=2 Calculate a₂ = a3 = a4 = b₂ = b3 = || b4 = " y₂ (x) = ∞ = x + -Σbnx", n=2 Cn-1+ If the series y(x) = Σcx" is a solution of the differential equation 1y” − 5x²y + 2y = 0, then Cn+2 = - n=0 Cn, n = 1,2,... A general solution of the same equation can be written as y(x) = C₁Y₁ (x) + C₁Y₂(x), where ∞ y (x) = 1 + 2 anx", Σ n=2 Calculate a₂ = a3 = a4 = b₂ = b3 = || b4 = " y₂ (x) = ∞ = x + -Σbnx", 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 ... View the full answer
Related Book For
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
Posted Date:
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