II. Solve the following Bernoulli's equations. 1. y'(1) = 3y - y. Answer. y= I+cr and y= 0. 2. y' -y = y*, y(2) =-2. 2x Answer. y= 2-x 3. xy' + y+ xy = 0, y(1) = 2. Answer. y= X(1+2 in x) 4. y' + y = xy', y(0) = -1. Answer. y=- dy - +2x %3D dx y Answer. y =tV-1– 2x + ce2x, 6. y' +xVỹ = 3y. Answer. y= - (;+*, and y = 0. +( + + ce«)°. Hint. When dividing the equation by Vy, one needs to check if y - 0 is a solution, and indeed it is. 7. y' +y = -xy, Answer. y= - ce-x-1 ,and y 0. 8. y' + xy = y', y(1) = -! Answer. y= - 1.7. Numerical Solution by Euler's Method 9. The equation 35 dy y + 2x dx could not be solved in the preceding problem set because it is not homoge- neous. Can you solve it now? Answer. y =tVcex – 2x – 1. 10. y' -ex + y. Answer. y= te'Vx + c. . 11. Solve the Gompertz population model (a and b are positive constants) dx =x (a - bln x), x>1. Hint. Setting y = In x, obtain y' = a - by. Answer. x(t) qa/bce -. 12. Solve x(y - e) + 2 = 0. Hint. Divide the equation by e" and then set u = e"Y, obtaining a linear equa- tion for v = v(x). Answer. y=- In (x + ex)

6. The wind chill factor is the temperature, in degrees Fahrenheit (°F), a human feels based on the air temperature in degrees Fahrenheit, and the wind velocity, v, in miles per hour. If the air temperature is 40°F, then the wind chill is given by w(v) = 60.6 – 18.64v0.16. Find w'(30). Use correct units to explain the meaning of w'(30) in terms of wind chill.

1. Solve the equation on the interval 0s0<2x. 4sin 0-3=0 元 2r O A. 3'3 I 5x O B. 6 6 1 5x 7x 11 C. 9. 6. I 2x 4x 5T O D. 3 3 3 3

Hey the problem in part a states that the substitution is v= -(y'/y) can you please help me out?