Find the general solution of the differential equation y'' - 25y = -75t + 50t². NOTE: Use t as the independent variable. Use c₁ and c₂ as arbitrary constants.
a) y(t) = -3t² + 4t + c1e⁵ᵗ + c₂e⁻⁵ᵗ
b) y(t) = -3t² + 4t + c1e⁵ᵗ - c₂e⁻⁵ᵗ
c) y(t) = 3t² + 4t + c1e⁻⁵ᵗ + c₂e⁵ᵗ
d) y(t) = 3t² + 4t + c1e⁻⁵ᵗ) - c₂e⁵ᵗ