Find y as a function of t if y" + 14y' + 85y = 0, y(0) = 9, y'(0) = 8. y(t) =

Step-by-step explanation:

The Given diffrential equation can be written as follows

Solving the auxiliary equation we get

Comparing with the standard quadratic equation we get

Using the values we get the roots as

The roots are imaginary and conjugate

For a auxillary equation with roots the solution is given by

Applying values we get the solution of the equation as

....................(i)

here are constants whose values shall be obtained using the given boundary conditions y(0) = 9 ; y'(0) = 8

In equation i putting x = 0 we get

9 =

Now we have

Now y'(0) = 8

Thus we get

Solving for we get

Thus the solution becomes

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent