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1. Find the General Solution and the Particular Solution to the following differential equa- tion: dy − (sinh r)y = (3r?)ecoshr, g(0)=e dx (All steps in the calculations must be clearly shown.) 2. Consider the second-order differential equation d²x dx +a- + b²x = 0 (a, b positive real constants) dt² dt (a) Find the characteristic equation and determine the conditions on a, b to obtain subcritical damping. (b) If a = b = 2, find the particular solution which satisfies x = 3 and t = 0. (All steps in the calculations must be clearly shown.) d.x dt = -2 when

1. Find the General Solution and the Particular Solution to the following differential equa- tion: dy − (sinh r)y = (3r?)ecoshr, g(0)=e dx (All steps in the calculations must be clearly shown.) 2. Consider the second-order differential equation d²x dx +a- + b²x = 0 (a, b positive real constants) dt² dt (a) Find the characteristic equation and determine the conditions on a, b to obtain subcritical damping. (b) If a = b = 2, find the particular solution which satisfies x = 3 and t = 0. (All steps in the calculations must be clearly shown.) d.x dt = -2 when

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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Needed to be solved both question correctly in 1 hour and get the thumbs up please show me neat and clean work for it By hand solution needed If you did one I will not give you thumb's up Please do both questios in the order to get positive feedback
1. Find the General Solution and the Particular Solution to the following differential equa- tion: dy dx (All steps in the calculations must be clearly shown.) - (sinhr)y= (32²) ecosh r, y(0) = e 2. Consider the second-order differential equation d²x d.x +a- + b²x = 0 (a, b positive real constants) dt² dt (a) Find the characteristic equation and determine the conditions on a, b to obtain subcritical damping. (b) If a = b = 2, find the particular solution which satisfies x = 3 and t = 0. (All steps in the calculations must be clearly shown.) d.x dt = -2 when
Transcribed Image Text:1. Find the General Solution and the Particular Solution to the following differential equa- tion: dy dx (All steps in the calculations must be clearly shown.) - (sinhr)y= (32²) ecosh r, y(0) = e 2. Consider the second-order differential equation d²x d.x +a- + b²x = 0 (a, b positive real constants) dt² dt (a) Find the characteristic equation and determine the conditions on a, b to obtain subcritical damping. (b) If a = b = 2, find the particular solution which satisfies x = 3 and t = 0. (All steps in the calculations must be clearly shown.) d.x dt = -2 when
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