Question

obtain the general solution of auxiliary equation
y'' - 8y' + 17y =0 y(0)=4 y'(0)=-1

Answer 1

did you find the characteristic solution

Answer 2

r^2 -8r + 17=0
r = 4+i , 4 - i

Answer 3

ok so far?

Answer 4

the general solution is
y = e^(4x) (c1*cos x + c2*sinx)

Answer 5

here is a site that explains it
http://www.sosmath.com/diffeq/second/constantcof/constantcof.html

Answer 6

y(0)=4
y(0) = e^(4*0) ( c1 cos(0) + c2 sin(0)) = 1 ( c1 + 0 )
Therefore
c1 = 4
now take the derivative (use product rule)