Use Problem 55 in Exercises 1.1 and (2) and (3) of this section.

1. Find a function y = f (x) whose graph at each point (x, y) has the slope given by 8e^2x + 6x and has the y-intercept (0, 9).

2. Find a function y  f (x) whose second derivative is y'' = 12x  2 at each point (x, y) on its graph and y = -x + 5 is tangent to the graph at the point corresponding to x = 1.

Data from problem 55

Discuss, and illustrate with examples, how to solve differential equations of the forms dy/dx = f(x) and d²y/dx² / f (x).