Unless stated otherwise, the multiple-choice questions have only one correct answer.

1. (There may be more than one correct answer for this question)

Which of the equations are first order differential equations? y' = sin(x) In(y') = 3 y" = 3 y' + 3y = 6x +11 y" - 3y = 24ex + 3The differential equation 31' + my + 6:1: = 11m2 is choose your answer... V , choose your answer... v ,and choose your answer... What integral equation is equivalent to the initial value problem y' = f(x), y(xo) = yo? O y = yo + Ja f(t) dt y = yo - f(xo) + S f(t) dt O y = Si f(t) dt O y = -f(xo) + Sa f(t) dt\fSolvetheinitialvalue problem 3% = y,y(0) = 5. Ans: yoekx,where yo = and k = If the answer is a rational number but not an integer, type a/b, where a and b are integers with greatest common factor 1, and b > 0. Solve the initial value problem ay + 2y(x) = 11, y(0) = 1. Ans: a + beca, where a = type your answer.. b type your answer.. C type your answer... If the answer is a rational number but not an integer, type m, where m and n are integers with greatest common factor 1, and n > 0.1:! A 55kg cyclist on a 10kg bicycle starts coasting on level ground at 25m/s. Use 1) : voc H , where k is about 3.9kg/s. 1. About how far will the cyclist coast before reaching a complete stop? Ans: m (Round to the nearest tenth if necessary.) 2. How long will it take the cyclist's speed to drop to 1m/s? Ans: 5 (Round to the nearest hundredth if necessary.) A tank initially contains 100 gal of brine in which 50 g of salt are dissolved. A brine containing 2 g / gal of salt runs into the tank at the rate of 5 gal / min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 4 gal / min. Let y(t) be the amount of salt in the tank at time t in minutes. Then the rate of salt entering the tank satisfies a first order choose your answer... V differential system given by y' (t) + P(t)y(t) = Q(t), where P(t) is a choose your answer... and Q(t) is a choose your