Choose letter E if the answer is not in the choices 45-52. Answer the following to form the differential equation of the family of circle touching the y-axis at origin. 45. The equation of the circle satisfying the condition is a. (x-a) + y = a b. (x+a) + y' = a C. X + y? = d. x2 + (y-b) = a 46-47. Expanding the answer in 39 yields a. X? - ax - a + y? = a b. x2 - 2ax - a + y? = a C. X' +2ax - a + y? = a d. x2 - 2ax +y? = 0 48-49. 2a = a. x - ylx2 b. x + y? /x c. X - y' /x d. x + y/x 50-52. Differentiating both sides with respect to x. a. 2xyy' + x = y' b. 2xyy' + x = y c. 2xyy' - x = y' d. 2xyy' - x = yz 53-57 Find the general solution given: x dy/dx = -ys 53-54. Separating the variables will result to a. -dy/y = dx/x b. -dy/y5 = -dx/x5 c. -y/dy = x/dx d. -y/dy = -x/dx 55-56. What is the results when the answer in 53-54 will be integrated? a. -y /4 = x /4 + C b. -y /4= -x /4 + C c. -y' /4 = x* /4 + C d. -y* /4 = - x*/4 + C 57. The general solution is a. X - y = C b. x* + y' = C c. X'+ y'= C d. x - y' = C