dy/dx = 10exp(2x) - 4; when x = 0, y = 6. Find the value of y when x = 2.

First, we must evaluate what is given in the question. As it can be seen, the expression indicates that the problem consists of a first-order differential equation. We are also given the values of x and their respective y value. These indicate that the problem should be integrated and then solved to obtain the value for the integration constant. Finally, we must calculate the value of y for when x = 2. Following these steps, the differential equation can be integrated to give y = 1/210exp(2x) - 4x + C. We are given that y = 6 when x = 0, thus the value of C is calculated as C = 6 - 5exp(0) = 1. Thus the general expression of y is y = 5exp(2x) - 4x + 1. Substituting in the value of x = 2 gives y(2) = 5exp(22) - 42 + 1 = 5exp(4) - 7.