Solutions to Quiz 5 Question 1. ( 4 points) y (t) = e2t+y(t) dy(t) = e2t dt ey(t) dy(t) = ey(t) 1 ey(t) d(y(t) = e2t d(2t) + C ey(t) = 2 e2t dt + C 1 2t e + C. 2
Substituting the initial value y(1) = 2 to the above equation, we have e(2) = Then, 1 3 + C C
Solutions Quiz 4 of CAL1201b-01
Question 1: (4 points): Solve the initial value problem (x2 + 1)y + 2xy = x3 + x, y(0) = 2. The differential equation in the standard form: 3 3 2x 2x y + x2 +1 y = x2+x p(x) = x2 +1 and q(x) = x2 +x x +1 x +1
1 u du
2
F (x)
Answers to the quiz 3 of CAL1201b-01
Answer to question 1. (i) Solve the following character equation of A det|A rI| = r 2 r 2 = 0, we have r = 2 or r = 1. Therefore, the larger eigenvalue r = 2 is the long-term growth rate and the long-term percentage gr
Solution to Problem 1: Assume that the number of the young rat is x, the number of the female rat is y, and the number of the male rat is z. Then, we have: 1)Total number of the rate is 23 means: x + y + z = 23; 2)The total consumption of food is 376 g me
Solutions Quiz 5 of CAL1201b-01
Question 1 4 points Solve the IVP y (x) + 6y (x) + 9y(x) = 0, y(0) = 2, y (0) = 2. The auxiliary equation is: r2 + 6r + 9 = 0 r = 3 (repeated) So the general solution of the DE is: y(x) = C1 e3x + C2 xe3x The rst derivative
Solutions to Quiz 7 Solution to Question 1. x = x + y + 2 = x + 2x + 2t 1 + 2. x + x 2x = 2t + 1. Solve auxliary eqn. r 2 + r 2 = 0, r = 2, r = 1. xh (t) = C1 e2t + C2 et . Assume xp = At + B, a 2(At + B) = 2t + 1 A = 1, B = 1 xg (t) = C1 e2t + C2 et t 1.
Quiz 10 of Cal1301b-001 (Winter 2009) Name: Student #:
You have to show your work ! Use the back if you run out of space. 1. (i) (2 pts) A pea plan of genotype Ff is crossed with another pea plan with genotype ff. Find the probability for each of the thre
Quiz 9 of Cal1301b-001 (Winter 2009) Name: Student #:
You have to show your work ! Use the back if you run out of space. 1. (2 4 = 8 pts) A fair die is rolled twice. Find the probability that (i) both rolls are sixes (ii) none of the rolls is six; (iii) n
Solutions to Quiz 8 Let x and y be the populations (in thousands) of two species that share the same habitat. Their interactions are described by the following systems of differential equations. 1. Assume the interaction of the two species is competition: