# integrating factor for the differential equation

Question 1 4 pts Which of the following is the integrating factor for the differential equation x x + 2y = x3 + 3×2 + 2x? dy There is no integrating factor because the equation is nonlinear. O x2 + 3x + 2 2x Question 2 4 pts Which of the following describes the differential equation(x + 3) dx + (y + 2) dy = 0? Select all that apply. It is a linear equation. It is a separable equation. It is an exact equation. It is a homogeneous equation. Question 3 4 pts dy Which would be a suitable substitution for the differential equation dx + 2 2 -Y х 11- x = Uy u = y y = ux Our y-3 Question 4 4 pts What is the solution to the following differential equation? (2y3 + y + 4) dx + (6xy2 + x) dy = 0 2xy + xy = k f(x, y) = 2xy + xy + 4x 2xy + xy + 4x = k Of(x, y) = 2xy + xy Question 5 4 pts Suppose that the population of bacteria grows at a rate proportional to the number of bacteria at timet. Initially, there are P, bacteria. Two hours later, the number of bacteria doubled. If P(t) = Poekt is a model for the population at time t, then which of the following is our value for k? (Select] (1) k = In 2 (2) k = { In 2 (3) k = 2 Approximately how long does it take for the number of bacteria to triple? [Select] (a) 2.5 hours (b) 2.87 hours (c) 3.17 hours (d) 3.43 hours

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