Find y as a function of x if y7yy7y0 y07 y05 y0103 yxSolutio

Find y as a function of x if

y????7y???y?+7y=0,

y(0)=?7,  y?(0)=?5,  y??(0)=?103.
y(x)=

Solution

y\"\' -7y\"-y\'+7y=0

for finding the CF

m^3-7m^2-m+7=0

(m-1) (m^2-6m-7)=0

(m-1)(m+7)(m-1)=0

m=1,1,-7

Y=c1e^x+c2e^x+c3e^-7x

y(0)= -7

c1+c2+c3=-7

y\'(0)=-5

-5=c1+c2-7c3

y\"(0)

-103=c1+c2+49c3

c1+c2=7c3-5

7c3-5+c3=-7

8c3=-2

c3=-1/4