Verify that the given functions y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. t2y'' − 2y = 5t2 − 1, t > 0, y1(t) = t2, y2(t) = t−1

The number of revolutions of two pulleys is inversely proportional to their diameters. if a 24-inch diameter pulley making 400 revolutions per minute is belted to an 8-inch diameter pulley, find the number of revolutions per minute of the smaller pulley.

1. writing an equation for an exponential function by 2. a piece of paper that is 0.6 millimeter thick is folded. write an equation for the thickness t of the paper in millimeters as a function of the number n of folds. the equation is t(n)= 3. enter an equation for the function that includes the points. (-2, 2/5) and (-1,2)

Find an bif a = {3, 6, 9, 12) and b = {2, 4, 6, 8, 10).