a Mail 22:12 webwork.ticaret.edu.tr WorK Log Out WeBWorK 201 7Fall-ENG227 Hw5 6

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a Mail 22:12 webwork.ticaret.edu.tr WorK Log Out WeBWorK 201 7Fall-ENG227 Hw5 6 HWS: Problem 6 (1 pt) (a) Find the general solution to y"+3y'-Give your answer as and oto denote arbitrary constants Inyour answer, use and r the independent variable. Enter qas cl and as c2. help (equations ) (b) Find the particular solution that satisfies (0)-1 and (0)-1 help(equations) Note: You can earn partial credit on this problem Preview Answers Sum Anwers You have attempted this problem 0 times. You have unlimited attempts remaining. Page generated at 12/19/2017 at 08:18pm EET WeBWorK © 2000-2007 The weBworKProject

Explanation / Answer

Given equation y"+3y'=0. Take the coefficients of y",y',y and put them in equation ar2+br+c=0

=> r2 + 3r=0

=> r(r+3)=0  

which implies r=0, -3

Thus general solution is y = c1 e0t + c2 e-3t

or y= c1 + c2 e-3t

b) y(t) = c1 + c2 e-3t

taking derivative

y'(t) = -3 c2 e-3t

using initial conditions., we have

1= -3c2 => c2 =-1/3

and 1 = c1 + c2  => c1 = 4/3

thus y= 4/3 - 1/3 e-3t is the particular solution.

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