Only question 1 and 2 please.

1. Consider the first order differential equation y' 2 -1/3 (a) Find the general solution to this differential equation. (b) Find the particular solution to this differential equation so that when r = 0, y = 0. (c) If y = f(x) is a solution to this differential equation with domain (-oo, co), for what values of r is it differentiable? 2. Use the following desmos tool to look at the slope field for d .dy = y - r: https://www. desmos . com/ calculator/p7vd3cdmei (a) Sketch solution curves with initial conditions y = 1 when r = 0, y = 0 when I = 2, and y = 3 and r = -1. (b) Describe the end behavior of a solution curve as I - 00. (c) Describe the end behavior of a solution curve as r - -00. 3. Use implicit differentiation to show that x2 +y2 = 2 is a solution to the differential equation # = for any constant r. 4. Use separation of variables to find the particular solution to the differential equation dy dt = y'(1 + t ) for which y = 2 when t = 1