My particular form solution looks like At^2+Bt+C+Dsin(4t)+Ecos(4t)+Fe^(2t), I know this is correct.I keep getting sin(4t)*(-16D-16E+4D)+cos(4t)*9-16E+16D+4E) which reduces to sin(4t)*(-12D-16E)+cos(4t)*9-12E+16D) which gets me D=(-4/3)E and E=-47/18 which is wrong, I even plugged it into an online diffeq solver which shows D=2/5 and E=-3/10 respectively. So I know there's something wrong with my application of method of undetermined coefficients. Enter an equation (and, optionally, the initial conditions):y"+4y'+4y=8t^2+10cos(4t)+8e^(2t)For example, y"(x)+25y(x)=0, y(0)=1, y'(0)=2.dydxd²yWrite y' (2) instead of y" (x) instead of etc.dx²If the calculator did not compute something or you have identified an error, or you have asuggestion/feedback, please write it in the comments below.CALCULATEYour input: solve 4y(t) + 4y' (t) + y″ (t) = 8t² + 8e²t + 10 cos (4t)ANSWER2 sin (4t)5e2ty(t) = 2t²4t+ (C₁ + С₂t) e¯ + +23 cos (4t)10+3 [19] Consider (*) y" +4y' + 4y = 8t² + 10 cos(4t) + 8e²¹.(a) Find the complementary solutions ye(t) of (*).(b) If one uses the method of undetermined coefficients to find a particular solution y(t)of (*), what is the suitable form of the trial solution y(t)?(c) Find a particular solution y(t) of (*).

Answered: Image /qna-images/answer/c754380c-eb81-450c-b82a-c3b93d889622.jpg

[19] Consider (*) y" + 4y + 4y = 8t² + 10 cos(4t) + 8e²¹. (a) Find the complementary solutions ye(t) of (*). (b) If one uses the method of undetermined coefficients to find a particular solution y(t) of (*), what is the suitable form of the trial solution y(t)? (c) Find a particular solution y(t) of (*).

[19] Consider () y" + 4y + 4y = 8t² + 10 cos(4t) + 8e²¹. (a) Find the complementary solutions ye(t) of (). (b) If one uses the method of undetermined coefficients to find a particular solution y(t) of (), what is the suitable form of the trial solution y(t)? (c) Find a particular solution y(t) of ().

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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