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(18pts) Give the general solution of the equation Y" + 2y' + y = 0 Give the form of the particular solutions (but do not solve for the coefficients!) of y...

Question

(18pts) Give the general solution of the equation Y" + 2y' + y = 0 Give the form of the particular solutions (but do not solve for the coefficients!) of y" + 2y +y = 3e2t + 5e-t + 3.

(18pts) Give the general solution of the equation Y" + 2y' + y = 0 Give the form of the particular solutions (but do not solve for the coefficients!) of y" + 2y +y = 3e2t + 5e-t + 3.



Answers

Find the general solution of the given equation. $$y^{\prime \prime}-2 y^{\prime}+3 y=0$$

Hello, everyone. In this given version, we have toe solve the initial value problem. The question is why devilish minus six Swedish plus 10 by it's a question and to initial conditions are given. That is wise. You guys too. And why does judo is three right? So first real light oxidant equation. So you get ice with minus six hour plus tenets Request ejido on the routes off. These equations are six plus minus and the 36 minus 40 divided by toe which comes out Toby six Celtics comes out to be three plus minus iota. So these are the 32 off the Given the question, since the roots are imaginary roots. So we have the general solution that is to the body X See one Cosby X plus C to sign bx tonight. Now, uh, a question. This is given the book so we'll plug the values from the roots that is is request to three and basic was too one like so it took about three x see, even cortex plus C to cynics. Now we have to find the values of C one and C two to find the value of C one and C two, We have toe put initial conditions. So why did you go? Is equal to which is equals to U to the power ejido. See you on cost you plus C to sign Jill. So this will give the u. N. Has to like now we will differentiate it. So when we differentiate the VX, we get virus access I hated about three x minus even cynics plus C two Cossacks plus three to the Power three x See you on Cossacks, Stephen cause t a X. So this even cause three X plus Ito Synnex. Right now we have the second initial value problem. That is why the studio is equal to three. So we get to the college. Edo Um minus even signed judo plus C to cost, you know, plus three to depart Judo C one cause street off Aceto Sandretto Like eso, this will result in, say, two plus 37 We know the value off Stephen. That s e questo. So c two plus, So this will give the result off Saito a spine astri Wright. Now we can put substitute the values off C one and C two in the general form. So we get wires created about three X to Cossacks minus three. Cynics. Right. So the sisters solution for the initial value problem.

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