Question

_D_6 The set of critical points of the autonomous equation y' = y(2-y) are: A (0.2.-2) B (0) C2) D.(0.2) (0,3,-3) D_7. The set of critical points (or equilibrium points) of the equation y'=yl - 9y is: A (0) C.-99) D_8. Which of the following is a stable point of ' (-1)? A0 B. 1 C andu1 D. Neither is stable F 9 True or False) The equation y + xy +x+yi b le Writer for true or F forse in the space next to the problem number of separable expressitasy- gy) The expression x + xy + x + y can be factored, but not as we would wish to F 10 True or False) The equation y a rate Writer for true or F for false in the space next to the problem number of separable, expressitas y (x) 0) **1 cannot be factored as f(x)g(x). Canes-be factored that way? PROBLEMS: Please show your work in the space provided. 1. A tank originally containing 60 galons of pure water receives brine salt-water) containing 0.5 lb per galon at a rate of 4 galons per minute. The solution is rapidly moved and pumped out of the tank at a rate of Salons per minute Write a diferential equation (including its initial conditions for Act). the amount of salt in the tank fort >0. V = 60; (0) = 0; 4: 0.5: Tout 5 The model is rate of salt in-rate of salt out -4-05-5 V) The volume at any time is V(t) = 60 + (4-5). Hence, The correct IP for this situation is Use separation of variables to solve the following equations: WE WILL GO OVER THESE IN CLASS TOMORROW 2 =(x+1) 3 k (Q-70): k a constant 4 +2p=1: p(O) = 10 5 -7- (1) - 0 6. xy - 3y + x - 3)dy - (x +2y - x - 2)dx=0

Answer 1

© y'= y-y) Is of form y'=f(y) where fry)= y*2-4): for critical points fry): 0 = yco-)=0 = 4=0,0,2 Ans;-() ie 10,2% are critical points ② y'= y²qy hure fly) = y²ay = 4(429) For the critical points flly) = 0 =) (4²9)=0 →y (9-3)(y+3)=0 =) y=0,3,-3 Ans:- (D) u's ucu-1 u= flu) for critical points fu)=0 4424-0-0 4=0,011 f(4) = 4²4² flu) = 34²-24 fius) = 360-260)= 0 =) 420 Is semistable auso -) 4=1 is unstable fla) = 301)-201) = 1 > al 451 ito 0 Ans:-(0) Neiller Is stable g'- . 82/ = e^x} - 328 which seperable can be y'=a’tay+aty: y'= x(4+41+ (x+y) y's (1+y)(a +12 which is not seperable false. (1) written as y'= f().919): here f(n) = e?? : 914)=e y'= eley True