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" - 4y =0; y₁ = e²x, y₂ = 2x; y(0) = 2, y'(0) = 0 Why is the function y₁ = ²x a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice. A. The function y₁ = ²x is a solution because when the function and its second derivative, y₁"= 4e²x, are substituted into the equation, the result is a true statement. OB. The function y₁ = 2x 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 = -2x a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice. The function y₂ =e-2x is a solution because when the function and its second derivative, y₂'' = 4e-2x, are substituted into the equation, the result is a true statement. OB. The function y₂ = 2x 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) = 2 and y'(0)=0 is y=.