Final answer:
The question involves solving a second-order linear ordinary differential equation (ODE) in Mathematics at the college level. The ODE is a Cauchy-Euler equation, typically solved by finding the characteristic polynomial's roots and a particular solution, which combines for the general solution.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on differential equations. This is typically a topic studied at the college level. The student's question asks to find the general solution of the equation t²y'' - ty' + y = t², for t > 0, which is a second-order linear ordinary differential equation (ODE).
To solve this ODE, we can identify that it is a Cauchy-Euler equation, which can be solved by assuming a solution of the form y = t^m. After substituting this into the ODE and solving for m, we find the associated homogeneous equation's characteristic polynomial and its roots. Then, the general solution to the homogeneous equation can be written in terms of these roots. Since the right side is a function of t, it is a non-homogeneous ODE, so we also need to find a particular solution. Once the particular solution is found, it is added to the general solution of the homogeneous equation to get the total general solution for the ODE.
The reference information provided is not directly applicable to solving the given ODE, as it seems to pertain to kinematic equations in physics. Calculating acceleration, time, or velocity from kinematic equations is a different process from solving an ordinary differential equation in mathematics.