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 8e2x + 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).
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