Question 1 dx Condsider the differential equation -= (1 -2x)y . Ify = 10 and x = 1, find an equation for y. Your answer: O V= 10ex-x2 O y=ex-x2 O V= 10+ ex-x2 O y=ex- x2 + 10 O V= X- x-+10Question 2 UV_V Find the particular solution to the differential equation 0' when x =1 and y = 6. x x Your answer: 0 Y=E o v=x+|n(6) O y=x O V=5X Question 3 Select the differential equation that matches the given slope eld. Your answer: O %X{y+1)2 O %x{y+n i=0\"? 0 G)! X2 W x2 Question 4 Which of the following is the general solution to the diffential equation dy 8x = dx V Your answer: O V= 1V8x+c O y= 8x+c O V= Ce 4x2 O V= + V 4 x- + cQuestion 5 A calculus student attempted to solve the differential equation -= 2xy with initial condition y = 3 when x = 0. In which step if any, does an error first appear. Step 1: S = dy = S 2x dx Step 2: Inly| = x2 + C Step 3: ly| = ex + C Step 4: Since y = 3 when x = 0, 3 = e + C. Step 5: y = -ex- +2 Your answer: O Step 1 O Step 2 O Step 3 O Step 4 O Step 5 O There is no error in this solution.Question 6 Which of the following is the general solution to the differential equation dy sin(t) dt 3y2 Your answer: O V=(- cos(t) + c)3 O V= tv-cos(t) + c O y= Ce-cos(1) O y=V-cos(t) + cQuestion 7 61 1 5 X -6 -5 -4 -3 3 -3 -5 Select the differential equation that matches the given slope field. Your answer: dy O dx ( x - 4)2 dy V O dx X - 4 dy (x - 4)2 O dx V dy O = - dx X - 4Question 8 Select the differential equation that matches the given slope eld. Your answer: Question 9 During a certain epidemic, the number of people that are infected at any time increases at a rate proportional to the number of people that are infected at that time. If 500 people are infected when the epidemic is first discovered, and 800 people are infected 5 days later, how many people are infected 10 days after the epidemic is first discovered? Your answer: O 1,170 1,280 O 1,100 O 1,225 Clear answer1 2 3 4 5 6 7 8 9 10 Question 10 Find the particular solution y = f(x) for the differential equation -= 106y when x = 0 and y = -15. dx Your answer: O V= 106e-15x O y= 106x - 15 O V= v 106x - 15 O V= - 15e 106x Clear