A homogeneous second-order linear differential equation, two functions y₁ and y₂, and a pair of initial conditions are given. First verify that y₁ and y₂ are solutions of the differential equation. Then find a particular solution of the form y=C₁Y₁ + C₂Y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x. y" + 16y=0; y₁ = cos (4x), y₂ = sin(4x); y(0) = 9, y'(0) = 3 (...) Why is the function y₁ = cos(4x) a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice. (Type an expression using x as the variable.) A. The function y₁ = cos (4x) is a solution because when the function and its second derivative, y₁" = - 16 cos (4x), are substituted into the equation, the result is a true statement. OB. The function y₁ = cos(4x) 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 y₂ = sin(4x) a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice. A. The function y₂ = sin(4x) is a solution because when the function and its second derivative, y₂"= -16 sin(4x), are substituted into the equation, the result is a true statement. B. The function y₂ = sin(4x) is a solution because when the function and its indefinite integral, , are substituted into the equation, the result is a true statement. The particular solution of the form y=c₁Y₁ + C₂Y₂ that satisfies the initial conditions y(0) = 9 and y'(0) = 3 is y=