Obtain the general solution for the following non - homogenous differential equation (use the wronskian method): y - y - 4y + 4y = 12 e - t evaluate the laplace transform of f(t) defined by: f(t) = solve the following initial value problem by using laplace transform: y + 0.2y + 4.01y = where: y(0) = 0 and y(0) = 2 solve the following differential equation: y + y = r(t) where: y(0) = 0 and y(0) = 0 when r(t) is a delayed impulse function given as: r(t) = 4 delta(t - 2 pi). when r(t) is a delayed step function given as: r(t) = u(t - 2 pi). show that the following ode is exact and solve it: cos (x + y) dx + {3y2 + 2y + cos (x + y)) dy = 0 solve the following ode. y' sin 2y + x cos 2y = 2x solve the following ode using integrating factor (x4 + y2) dx - xy dy = 0, y(2) = 1

What is the equation of the line in point-slope form? y+ 4 = 1/2(x+4) y-4 = 1/2(x + 4) y-0 = 2(x - 4) y-4 = 2(8-0)

(c) compare the results of parts (a) and (b). in general, how do you think the mode, median, and mean are affected when each data value in a set is multiplied by the same constant? multiplying each data value by the same constant c results in the mode, median, and mean increasing by a factor of c. multiplying each data value by the same constant c results in the mode, median, and mean remaining the same. multiplying each data value by the same constant c results in the mode, median, and mean decreasing by a factor of c. there is no distinct pattern when each data value is multiplied by the same constant. (d) suppose you have information about average heights of a random sample of airline passengers. the mode is 65 inches, the median is 72 inches, and the mean is 65 inches. to convert the data into centimeters, multiply each data value by 2.54. what are the values of the mode, median, and mean in centimeters? (enter your answers to two decimal places.) mode cm median cm mean cm in this problem, we explore the effect on the mean, median, and mode of multiplying each data value by the same number. consider the following data set 7, 7, 8, 11, 15. (a) compute the mode, median, and mean. (enter your answers to one (1) decimal places.) mean value = median = mode = (b) multiply 3 to each of the data values. compute the mode, median, and mean. (enter your answers to one (1) decimal places.) mean value = median = mode = --

Which of the following will form the composite function?