Q3. Suppose that the C2 function z = f(x, y) satisfies the differential equation a2 z 22. a 22-2 + 26 0 axdy ay2 where a, b, c are nonzero real numbers such that b2 - ac = 0. Show that if we let x = a + b and y = t, then z satisfies the simpler equation 22 z at2 = a for some constant a. Determine a explicitly. [Note: Using this, we can now easily find all functions that satisfy the original differential equation. Do you see how? (This is not part of the assignment and does not need to be submitted.)]