I attached the soloution that u gave for first 3 parts they said to find the solution of y(t) And also state briefly how your solouution is correct uh need go find all parts and plz have a look what they said to solve plzAlso don't reject this plz Six second-order equations and four y(t)-graphs are given below. For each y(t)-graph, determine the second-orderequation for which y(t) is a solution, and state briefly how you know your choice is correct. You shoulddo this exercise WITHOUT using technology.d²yd(i) +16y=10dt²+16y=-10+ 16y = 5 cos(3t)d'yd²y(iv)+ 14y = 2 cos(4t)+ 16y= = cos(4t)+2dy +16y=dt2dt(b)-2+Cm-2+म2+(d)Wi27y(t)-graphs for Exercise 3.(vi)AMAcos(4t) Answer)i) day +168 = 10df 2The associated homogeneousequation is:d²y +16y=0The auxiliary equation of the homogeneous differentialequationm² +16=0m = ± 24Therefore, the complementary solution of the equation is:y₁ = Acosq++ Bsin4t&p=aparticular solution as:Assume thewith respect tot: y = 0wo times differenziatisubstitute Jp any yo in cquation then we will get,ур0 +16a=10Then yp=&the general solution of the equation @is: y = GH+ Yp[4 = Acos 4t + Bgn 4+ + 5/8.i) dayde ² +169 = -10The particuler solution foryp = - FTherefore, thesolution of the given equation is:y = A los 4t + 1asin 4t - 5/8+164 = 5 cas (36)the particular solution for given differential equalVp = _gacos (36)-9b3in (34)y'p in given equation:andcos (st) - 9bsin(31) + 16 (acos (at) + bsin (3+) = 5 cas (36)(-99 +16 a ) cos( 3(-) + (-96-+166) Sin (3+) = 5 cos (34)7a (os (31) + 7bsin (at) = 5 (os(3+)a=5/7, b=0we get,Therefore, theParticular solution is yp = 5/7 (as (34)The solution of the given D.E ism) dayAssume2 علىgiventhe x differential equation is 8is yp = acos (36) + bsin (at)substituti ypy = A los 4+ + B sin4+ + 5/7 cos (36).

Given second-order differential equation and four y(t) graphs. To find: For each y(t) graph…

Six second-order equations and four y(t)-graphs are given below. For each y(t)-graph, determine the second-order equation for which y(t) is a solution, and state briefly how you know your choice is correct. You should do this exercise WITHOUT using technology. d²y d (i) +16y=10 dt² +16y=-10 + 16y = 5 cos(3t) dt² d'y d²y (iv) +14y = 2 cos(4t) +16y= cos(4t) = +2dy + 16y= dt2 dt (a) (b) (v) -2+ (vi) AM cos(4t)

Six second-order equations and four y(t)-graphs are given below. For each y(t)-graph, determine the second-order equation for which y(t) is a solution, and state briefly how you know your choice is correct. You should do this exercise WITHOUT using technology. d²y d (i) +16y=10 dt² +16y=-10 + 16y = 5 cos(3t) dt² d'y d²y (iv) +14y = 2 cos(4t) +16y= cos(4t) = +2dy + 16y= dt2 dt (a) (b) (v) -2+ (vi) AM cos(4t)

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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