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        

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

i hope this you!