Final answer:
The general solution of the given differential equation y'' + 4y = t² e^(3t) + 3 is found by solving the quadratic equation and substituting the values of t into the general equation for y.
Step-by-step explanation:
The general solution of the given differential equation y'' + 4y = t² e^(3t) + 3 is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 4, b = 0, and c = 3. By using the quadratic formula, we can find the solutions for t. After finding the values of t, we can substitute them into the general equation y = c₁e^(rt) + c₂te^(rt) to find the general solution of the differential equation.