Verified answer

If the two roots of the characteristic equation are k1 and k2, then we are told that:

k1 + k2 = 94 and k1*k2 = 2013.

k2 = 2013/k1

k1 + (2013/k1) - 94 = 0

We know that k1 cannot equal zero (else the product of k1*k2 would be zero), so we can multiply this last equation by k1:

k1^2 - 94*k1 + 2013 = 0

(k1 - 33)(k1 - 61) = 0

k1 = 33 or 61,

Plugging these results into the constraint that k1 + k2 = 94, we find that k2 = 61 or 33, which are the values for k1 we already found.

The solution to the differential equation is then:

y(t) = a*exp(33t) + b*exp(61t)

where a and b are the constants of integration.