1. State the order and the linearity of the given differential equations: (5 points) i. yx " - (x' ) "+x=0 (1 point) ii. Yt "+ yt'+y= sin (t+ y) (2 point) iii. y" - (1 -y? ) y' + y=0 (1 point) iv. x"( sin B) + x' (cos B) = 0 (1 point) 2. Use differential equations to model the following processes below: (5 points) The differential equation dP/dt = k (cost) k where k is a positive constant, is a model of human population P(t) of a certain community. Discuss an interpretation of the solution of this equation. Analyze the solution to the differential equation and elaborate on the population. 3. Given are the solutions(i) to (iv) and the DE, match the correct solution to the DEs: (5 points) yx" - x' = 0 where (i) x = 0; (ii) x = 2y; (iii) x = 2; (iv) x = 2y? (v) x = 2y3 4. Solve the given differential equation by separation of variables: (5 points) y x' = x - xy 5. Solve the given IVP by the method of separation of variables: (5 points) (1 + x#) dy + (1 + 4y2) x dx = 0 subject to IC: y(2) = 0