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y" - 2x² + 4xy = 0

y" - 2x² + 4xy = 0

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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I need detailed explanation solving this problem (a) from Engineering Mathematics, please.

Solve the following differential equation (a) y" — 2x² + 4xy = 0 (b) y" + y sin x = X Note: The term ysinx becomes product of two power series, it's more difficult to derive the recurrence equation. In this case, you can simply collection of few like- power term (n=0, 1, 2, 3) (c) (x² + 1)y" + xy' - y = 0 1 Note: These two function, p(x) = X x²+1 -1 and q(x) = x²+₁² are actually analytic (i.e., +1' they have convergent Taylor series expansions, so they can be represented by power series), meaning you can still use power series method for this problem. No need to use the Frobenius method.)
Transcribed Image Text:Solve the following differential equation (a) y" — 2x² + 4xy = 0 (b) y" + y sin x = X Note: The term ysinx becomes product of two power series, it's more difficult to derive the recurrence equation. In this case, you can simply collection of few like- power term (n=0, 1, 2, 3) (c) (x² + 1)y" + xy' - y = 0 1 Note: These two function, p(x) = X x²+1 -1 and q(x) = x²+₁² are actually analytic (i.e., +1' they have convergent Taylor series expansions, so they can be represented by power series), meaning you can still use power series method for this problem. No need to use the Frobenius method.)
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