7. Please solve without a calculator Q7) (Series solutions near a regular singular point) The following differential equationay" + (1 – a)y/ – 2y = 0, a > 0,0. i) Start with the series solution y = E , and"+r and findthe recurrence relation for any exponent r. ii) Determine the indicial equation and show that thehas a regular singular point at ro =roots of the indicial equation are equal. iii) For the root r1, find a formula for a, and write the seriessolution y1 (x).

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Description: 7. Please solve without a calculator Q7) (Series solutions near a regular singular point) The following differential equationay" + (1 – a)y/ – 2y = 0, a > 0,0. i) Start with the series solution y = E , and"+r and findthe recurrence relation for any e

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Q7) (Series solutions near a regular singular point) The following differential equation ry" + (1 – r)y – 2y = 0, r> 0, has a regular singular point at ro = 0. i) Start with the series solution y = Eo a,r"+r and find the recurrence relation for any exponent r. i) Determine the indicial equation and show that the roots of the indicial equation are equal. iii) For the root r1, find a formula for a, and write the series solution y1(x).

Q7) (Series solutions near a regular singular point) The following differential equation ry" + (1 – r)y – 2y = 0, r> 0, has a regular singular point at ro = 0. i) Start with the series solution y = Eo a,r"+r and find the recurrence relation for any exponent r. i) Determine the indicial equation and show that the roots of the indicial equation are equal. iii) For the root r1, find a formula for a, and write the series solution y1(x).

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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