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Consider this initial-value problem: y" + 6xy - 18y = 0, y(0) = 4, y (0) = 0. Assume a solution of this equation can be represented as a power series y(x) = Σ n=0 (i) Write down the values of these coefficients: Co = C4 = a = k= C₁ = i ,C5 = (ii) Write down the first four nonzero terms of the power series solution. y(x) = a + bxk + cxm + dx", where k

Consider this initial-value problem: y" + 6xy - 18y = 0, y(0) = 4, y (0) = 0. Assume a solution of this equation can be represented as a power series y(x) = Σ n=0 (i) Write down the values of these coefficients: Co = C4 = a = k= C₁ = i ,C5 = (ii) Write down the first four nonzero terms of the power series solution. y(x) = a + bxk + cxm + dx", where k

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider this initial-value problem: y" + 6xy - 18y = 0, y(0) = 4, y (0) = 0. Assume a solution of this equation can be represented as a power series y(x) = Σ n=0 (i) Write down the values of these coefficients: Co = C4 = a = k = C₁ = i ,C5 = (ii) Write down the first four nonzero terms of the power series solution. y(x) = a + bxk + cxm + dx", where k <m <n and b = , m = , C₂ = i , C6 = ,C= n = i C₂ = , d =
Transcribed Image Text:Consider this initial-value problem: y" + 6xy - 18y = 0, y(0) = 4, y (0) = 0. Assume a solution of this equation can be represented as a power series y(x) = Σ n=0 (i) Write down the values of these coefficients: Co = C4 = a = k = C₁ = i ,C5 = (ii) Write down the first four nonzero terms of the power series solution. y(x) = a + bxk + cxm + dx", where k <m <n and b = , m = , C₂ = i , C6 = ,C= n = i C₂ = , d =
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