# solve the IVP y"+2y'+17y=0.y(0)=1,y'(0)=-1 Thanks in advance. Show transcribed image text y'' + 2y' + 17y = 0, y(0) = 1, y'(0) = - 1

Question
solve the IVP y"+2y'+17y=0.y(0)=1,y'(0)=-1
Show transcribed image text y'' + 2y' + 17y = 0, y(0) = 1, y'(0) = - 1

2020-12-28
The characteristic equation is r^{2}+ 2r + 17 = 0
The roots of characteristic equation are : -1± 4i
Then the general solution of homogeneous equation is :.........(i)
Then $$\displaystyle{y}'{\left({0}\right)}=-{c}{1}{e}-{t}{\cos{{4}}}{t}-{4}{c}{1}{e}-{t}{\sin{{4}}}{t}-{c}{2}{e}-{t}{\sin{{4}}}{t}-{4}{c}{2}{e}-{t}{\cos{{4}}}{t}$$ .......(ii)
Using initial values in (i) and (ii), find c1 and c2 and then write the general solution.

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