A homogeneous second-order linear differential equation, two functions y, and y,, and a pair of initial conditions are given. First verify that y, and y, are solutions of the differential equation Then find a particular solution of the form = Cy, +Czy2 that satisfies the given initial conditions. Primes denote derivatives with respect to x y" +2y' +y = 0: y1 = e, y2 =xe * y(0) = 9, y'(0) = - 7 Why is the function y, = e a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice O A. The function y, = e -X is a solution because when the function, its first derivative y,'= and its second derivative, v."= are substituted into the equation, the result is a true statement O B. The function y, = ex is a solution because when the function and its indefinite integral are substituted into the equation, the result is a true statement Why is the function y, =xe -X a solution to the differential equation? Select the correct choice below and fill in the answer box to complete vour choice O A. The function y, =xe -X is a solution because when the function and its indefinite integral are substituted into the equation, the result is a true statement O B. The function y, =xe -X is a solution because when the function, its derivative y,= and its second derivative y,'= are substituted into the equation, the result is a true statement The particular solution of the form y = c, y, + c,y2 that satisfies the initial conditions y(0) = 9 and y'(0) = - 7 is y= Click to select your answer(s).