Part A. Determine whether the given first expression is the solution of the succeeding given ODE. (10pts) 1. y = 2 In x => xy" +y' =0 2. y = CicOS 2x + C2sin 2x + (2 => y"'+ 4y' = 0 3. x = - In t, y = cit + cat? => y"(x) + 3y'(x) + 2y = 0 Part B. Determine the equivalent ODE by eliminating the arbitrary constants. (10pts) 1. x3 - 3x2y = C 2. y = x cos (In x + c) 3. x = A sin (wt + B) , eliminate A and B having x as the dependent and t as the independent variablePart C. Find the general solution of the following ODE using variable separable. (10pts) 1. dy/dx + exty = 0 2. (x + 2) dx = (x +3) sin(y) cos(y) dy Il. Sketching the Family of Curves 1. Find the equivalent DE for all circles whose center is at P(0,1). Sketch the family of these circles. (10pts) 2. Find the equivalent DE for all vertical parabolas and sketch the family of these parabolas. (10pts) 3. Sketch the family of curves given by the equation 5(dy/dx) +2x = 3 and determine the equation of one of these curves which passes through P(0,0). (Sketch also the particular solution given by the point P) (10pts)