Final answer:
Without a specific differential equation and initial condition provided, it's not possible to find a unique solution. In kinematic problems, identifying known and unknown variables and applying the appropriate equation is essential for finding solutions.
Step-by-step explanation:
To find the unique solution of a differential equation satisfying an initial condition, one needs to have the specific differential equation and initial condition provided. However, the student has not provided these, and therefore, it's not possible to determine the solution without additional information. In general, a unique solution exists for a differential equation given an initial condition if the equation meets the criteria of the existence and uniqueness theorem, but we need the actual equation and condition to apply this.
When solving physics problems involving kinematic equations, the steps taken typically involve identifying known variables (like initial velocity, acceleration, time, etc.), determining the unknown variables, and then selecting the appropriate kinematic equation(s) that contain the unknown variable. This process allows for the calculation of the unknown. However, the number of unknowns must not exceed the number of equations available for a solvable scenario.