3. y" + 3y" — 4y = e` -2x - In Problems 10-4, use the method of undetermined coefficients to determine the form of a particular solution for the given equation.

3) Personal taxes Suppose that the percent of total personal income that is used to pay personal taxes is given by y = 0.034x2 – 0.044x + 12.642 where x is the number of years past 1990 (Source: Bureau of Economic Analysis, U.S. Department of Commerce). (a) Verify that x = 7 is a solution of 14 = 0.034x2 – 0.044x + 12.642. (b) Find the year or years when the percent of total per- sonal income used to pay personal taxes is 14.

On the basis of data from 1990 to 2006, the median income y in year x for men and women is approximated by the equations given below, where x = 0 corresponds to 1990 and y is in constant 2006 dollars. If these equations remain valid in the future, in what year will the median income of men and women be the same? Men: Women: - 237x + 2y = 63,300 - 850x + 3y = 46,199 The median income of men and women will be the same in the year

2. Solve the initial value problem x1 = x2, x2 = -x1-2x2 + 4e, x1(0) = 1, x2(0) = 0.

5. Solve IVP у" - 4y" + 7y - бу %3D 0, у(0) %3D 1, у'(0) — 0, у" (0) — 0

3. Give an explicit real value general solution to each of the following equations. a) x-6x" +8x= 2e-9t b) y"-y-2y = cost solutions of the the

A survey of the white and nonwhite population in a local area reveals the following annual trip frequencies to the nearest state park: X̄1 = 4.1 X̄2= 3.1 s21 = 14.3 s22= 12.0 N1= 20 N2= 16 Where the subscript '1' denotes the white population and the dubscript '2' denotes the nonwhite population. Please solve (d) and (e) as a-c have been solved in the previous question. (a) assume the variances are equal, and test the null hypothesis that there is no difference between the park-going frequences of whites and nonwhites (b) repeat the exercise, assuming that the variances are unequal (c) Find the p-value associated with the tests in parts (a) and (b) (d) Associated with the test in part (a), find a 95% confidence interval for the difference in means (e) repeat parts a-d, assuming sample sizes of n1= 24 and n2= 12

wouldn't there be a t in the second term of the general solution?

Nitin.jgfff

Solve the given LDE using the method of undetermined coefficients. Show your full solution.