dY Consider the linear system: dt Y. (a) Show that the two functions Y1(t) = () and Y2(t) : 2t) are solutions to the differential equation. (b) Show that the two solutions are linearly independent. = (; ") dY (c) Solve the IVP: dt Y, Y(0) =

An integrating factor for the linear differential equation Y- 2y : = 12x is u= | A. 2xe2x В. — 2 C.-2x D. In 2x O E. e Е. -2x

Consider the differential equation y'(t) = t" - 3y and the solution curve that passes through the point (3, – 1). What is the slope of the curve at (3, - 1)? The slope of the curve at (3, - 1) is. (Simplify your answer.)

Day traders typically buy and sell stocks (or other investment instruments) during the trading day and sell all investments by the end of the day. The following table shows the closing prices on September 22, 2015, of 12 stocks selected by your broker, Prudence Swift, as well as the change that day. Tech Stocks Close Change AAPL (Apple) $113.40 -1.81 ADBE (Adobe Systems) $84.66 1.34 EBAY (eBay) $25.61 -0.31 MSFT (Microsoft) $3.90 -0.21 S (Sprint) $4.40 0.02 WIFI (Boingo Wireless) $8.51 0.56 Non-Tech Stocks ANF (Abercrombie & Fitch) $21.81 -0.02 в (Воeing) $133.99 -2.03 F (Ford Motor Co.) $13.91 -0.40 GE (General Electric) $25.10 0.01 GIS (General Mills) $57.12 0.33 JNJ (Johnson & Johnson) $93.26 0.13 On the morning of September 22, 2015, Swift advised you to purchase a collection of three tech stocks and two non-tech stocks, all chosen at random from those listed in the table. You were to sell all the stocks at the end of the trading day. (a) How many possible collections are possible?…