Final answer:
The provided information describes a quadratic function rather than a differential equation. The initial condition is satisfied since f(3) calculates to 0 with the given function. Therefore, the particular solution is the function itself.
Step-by-step explanation:
The student is given a differential equation f(x) = (5x - 6)(5x + 6) and an initial condition f(3) = 0. To solve this problem, it is not a standard process of solving differential equations, instead, it appears to be a misunderstanding as the given information denotes a function rather than a differential equation.
Also, the initial condition given is already satisfied by the provided quadratic function because f(3) is indeed zero when calculated (3⋅5 - 6)(3⋅5 + 6) = (15 - 6)(15 + 6) = (9)(21) = 0. Therefore, assuming there was an error in how the question was formulated, the particular solution to f(x) that satisfies the given condition has been identified as the given quadratic function itself.