(19)(a) Suppsoe that y is a solution of the differential equationay" + by+cy 0.Let z(2) = y(r - ro) where ro is an arbitrary real mumber. Show thata:" + b'+ez 0.(b) Let a(r) = y(r – xo) and s2(2) = v2(x - ro), where vG = Cn + can is the general solution to apby +cy=0. Show that zG = +a is also a general solution of ay" + by + cy 0.

(19) (a) Suppsoe that y is a solution of the differential equation ay" + by+cy 0. Let 2(r) = y(r-ro) where ro is an arbitrary real mumber. Show that a:" + be' +es =0. (b) Let a() (r- ro) and s2() = va(* - ro), where va = Cn + can in the general solution to ap by +cy-0. Show that sa- +a is abo a general solution of ay" + by + cy -0.

(19) (a) Suppsoe that y is a solution of the differential equation ay" + by+cy 0. Let 2(r) = y(r-ro) where ro is an arbitrary real mumber. Show that a:" + be' +es =0. (b) Let a() (r- ro) and s2() = va(* - ro), where va = Cn + can in the general solution to ap by +cy-0. Show that sa- +a is abo a general solution of ay" + by + cy -0.

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

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(19)
(a) Suppsoe that y is a solution of the differential equation
ay" + by+cy 0.
Let z(2) = y(r - ro) where ro is an arbitrary real mumber. Show that
a:" + b'+ez 0.
(b) Let a(r) = y(r – xo) and s2(2) = v2(x - ro), where vG = Cn + can is the general solution to ap
by +cy=0. Show that zG = +a is also a general solution of ay" + by + cy 0.

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