Consider the following system of differential equations da V = 0, dt dy + 3x + 4y = 0. dt a) Write the system in matrix form and find the eigenvalues and eigenvectors, to obtain a solution in the form ( )= a()+ (1) M C₂ where C₁ and C₂ are constants. Give the values of X1, 31, A2 and 32. Enter your values such that A₁ A2- A₁ 9/1 3/2 Input all numbers as integers or fractions, not as decimals. Find the particular solution, expressed as a (t) and y(t), which satisfies the initial conditions (0) = 3, y(0) = -7. y(t)
