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Solve the differential equation below using series methods. (4 + x)y'+(1+4x)y'+(-5-2x)y = 0, y(0) = 3, y'(0) = 2 The first few terms of the series solution are: 3 4 y = a⁰ + a₁x + a²x² + α³x³ + α²x¹ Where: ao = a1 a2 az = a4 =

Solve the differential equation below using series methods. (4 + x)y'+(1+4x)y'+(-5-2x)y = 0, y(0) = 3, y'(0) = 2 The first few terms of the series solution are: 3 4 y = a⁰ + a₁x + a²x² + α³x³ + α²x¹ Where: ao = a1 a2 az = a4 =

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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Solve the differential equation below using series methods. (4 + x)y'+(1+4x)y'+(-5-2x)y = 0, y(0) = 3, y'(0) = 2 The first few terms of the series solution are: 3 4 y = a⁰ + a₁x + a²x² + α³x³ + α²x¹ Where: ao = a1 a2 az = a4 =
Transcribed Image Text:Solve the differential equation below using series methods. (4 + x)y'+(1+4x)y'+(-5-2x)y = 0, y(0) = 3, y'(0) = 2 The first few terms of the series solution are: 3 4 y = a⁰ + a₁x + a²x² + α³x³ + α²x¹ Where: ao = a1 a2 az = a4 =
Expert Solution
Step 1: Derivative of the series

Let the series solution of the above initial value problem be

y(x)=∑n=0∞anxn

Then 

y′=∑n=1∞nanxn−1

y″=∑n=2∞n(n−1)anxn−2

Now y(0)=a0  ,  y′(0)=a1

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