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(19) (a) Suppsoe that y is a solution of the differential equation ay" + by + cy -0. Let 2(2) - y(r- ro) where ro is an arbitrary real number. Show that a:" + be' +ez 0. (b) Let 1(r) wn(r-ro) and z2(r) = 2(r-zo), where yc Cn + ca2 is the general solution to ay" + by +cy 0. Show that se =1 +ea 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(2) - y(r- ro) where ro is an arbitrary real number. Show that a:" + be' +ez 0. (b) Let 1(r) wn(r-ro) and z2(r) = 2(r-zo), where yc Cn + ca2 is the general solution to ay" + by +cy 0. Show that se =1 +ea is also a general solution of ay" + by +cy 0.

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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(19) (a) Suppsoe that y is a solution of the differential equation ay" + by + cy = 0. Let :(2) = y(1 - ro) where ro is an arbitrary real number. Show that a:" + b:' + ez 0. (b) Let 1(2) = (r - ro) and z2(r) = y2(r - ro), where NG = Cn + c22 is the general solution to ay" + byf +cy = 0. Show that G = 1 +22 is also a general solution of ay" + by + cy 0.
Transcribed Image Text:(19) (a) Suppsoe that y is a solution of the differential equation ay" + by + cy = 0. Let :(2) = y(1 - ro) where ro is an arbitrary real number. Show that a:" + b:' + ez 0. (b) Let 1(2) = (r - ro) and z2(r) = y2(r - ro), where NG = Cn + c22 is the general solution to ay" + byf +cy = 0. Show that G = 1 +22 is also a general solution of ay" + by + cy 0.
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