Three solutions of a second-order linear equation L [y] = g(t) and ψ₁(t) = 3eᵗ + eᵗ², ψ_₂(t) = 7e'+eᵗ² and ψ₃ (t) = 5eᵗ + eᵗ + eᵗ².
Find the solution of the initial-value problem L[y] = g; y(0) = 1, y'(0) = 2.