Differential Equation HW

Consider the differential equation ty' + (t + 1)y = 2te −t

which has the general solution y(t) =

e −t

(t + C/t), for any value of the constant, C. Which solution satisfies the initial condition y(1)

= 1/e ?

Plot the direction field for the equation y' = y 2

− t. In the rectangle R = {(t, y): −2 ≤ t ≤ 10, −4

≤ y ≤ 4}.