Find y as a function of t if 49y" + 42y' + 13y = 0, y(0) = 8, y'(0) = 5. y(t) =

Step-by-step explanation:

Given:

  49y''+42y'+13y=0    ,y(0)=8,y'(0)=5  

Lets take  a y''+by'+c=0  is a differential equation.

So auxiliary equation will be

So according to given problem our  auxiliary equation will be

Then the roots of above equation

  But D in the above question is negative so the roots of equation will be imaginary ().

By solving m= -0.428+0.285i  , -0.428-0.285i,

  m=

So

So now by using giving condition we will find

So        

i believe the answer is letter c) 8

step-by-step explanation:

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.