Given the initial value problem x₁'=-_₂x₁ x_₂, show that if a₁₁, a₁_₂, a_₂₁, and a_₂_₂ are constants with a₁_₂ and a_₂₁ not both zero, and if the functions g₁ and g_₂ are differentiable, then what is the solution to the initial value problem?