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(1) Show that z = A cosh(wz)+ B sinh(wr) satisfies the differential equation z" - w²r = 0. (2) given that y(t) = ae' + bw" with y(0) = 2 and /(0) = 2, find the values of a and b. (3) The general solution to second-order differential equation 5y" = 2y is in the form y(x) = ce" + c, where e and o are constants. Find the value of r. %3D

(1) Show that z = A cosh(wz)+ B sinh(wr) satisfies the differential equation z" - w²r = 0. (2) given that y(t) = ae' + bw" with y(0) = 2 and /(0) = 2, find the values of a and b. (3) The general solution to second-order differential equation 5y" = 2y is in the form y(x) = ce" + c, where e and o are constants. Find the value of r. %3D

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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(1) Show that z = A cosh(wx)+B sinh(wz) satisfies the differential equation z"-w²r =0. (2) given that y(t) = ae' + be with y(0) = 2 and y(0) = 2, find the values of a and b. (3) The general solution to second-order differential equation 5y" = 2y is in the form y(x) = ce + C, where e and cz are constants. Find the value of r. %3D
Transcribed Image Text:(1) Show that z = A cosh(wx)+B sinh(wz) satisfies the differential equation z"-w²r =0. (2) given that y(t) = ae' + be with y(0) = 2 and y(0) = 2, find the values of a and b. (3) The general solution to second-order differential equation 5y" = 2y is in the form y(x) = ce + C, where e and cz are constants. Find the value of r. %3D
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