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Homework 4-3: Problem 4 Previous Problem List Next (1 point) Find the general solution to y" + 4y' + 29y = 0. In your answer, use e, and to denote arbitrary constants and t the independent variable. Enter as c1 ando as c2. Preview My Answers Submit Answers You have attempted this problem 0 times You have unlimited attempts remaining Email instructor Page generated at 03/15/2020 at 09:28pm EDT 1998-2015 theme math 4 ww_version 2.10 pg_version 2.10The We Work Project WeWork

Answer 1

The the for characteristic equation differential equation es day y te p det man + ay=0 1 & yt pylt Qy z o. - is written as 2²+Pr+0=0 where p, and of are constant So, for given differential equation y" +44 +29y=0

Characteristic equation is я? + 4 A+ 29 - Я— 4+ ) 42-4 X29 2 Я = - 4€ 16 – 116 2 эх= - 4t J-Joo 2 ЭХ: -4t lot 2 эЯ- — 2+ Si

If loves 7 characteristie equation are imaginary like you l=&=iß, then solution is given as y(t) = 4 estipt to cz ex-cost #y(t) = eat (a cospt + C sinßt)

So, for deres {=-2 I is solution is given as y(t) = 9+15) t a lezist =y(t) = ēl * CG cos(5+)+ 4 sin(54)) This is the requirea general solution