Final answer:
To solve the initial value problem and find its explicit solution, we need to solve the differential equation and find the equation that represents the solution. The process involves using calculus and trigonometric functions to determine the values of the constants. The solution can be verified by substituting and taking derivatives.
Step-by-step explanation:
The given problem is asking for the solution of the initial value problem in explicit form. To solve this problem, we need to solve the differential equation and find the equation that represents the solution. The provided information mentions substitution and derivative steps to verify the solution, indicating that it involves calculus. The explicit form of the solution involves finding the values of the constants and using trigonometric functions.