1) Consider the equation (x2 + 1)y" – 6y = 0 Let y(x) = E=-0 Cnx" be a solution and -(k – 3) - Ck k + 1 Ck+2 = k = 2,3,4, ... С2 — ЗСо — 0, Сі— Сз — 0 Find the general power series solution to the differential equation. Give the first 3 nonzero terms of each independent power series solution.

1) Consider the equation (x2 + 1)y" – 6y = 0 Let y(x) = E=-0 Cnx" be a solution and -(k – 3) - Ck k + 1 Ck+2 = k = 2,3,4, ... С2 — ЗСо — 0, Сі— Сз — 0 Find the general power series solution to the differential equation. Give the first 3 nonzero terms of each independent power series solution.

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

1) Consider the equation (x2 + 1)y" – 6y = 0
Let y(x) = E-o Cnx" be a solution and
-(k – 3)
Ck+2
Ck , k= 2,3,4, ...
k + 1
C2 – 3co = 0 , C1 – C3 = 0
Find the general power series solution to the differential equation. Give the first 3 nonzero terms of each independent
power series solution.

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