StellarA particular solution is the specific solution to a differential equation that passes through a given point or satisfies an initial condition. After finding the general solution, we use the initial condition to solve for the constant C. This turns the whole family of possible solutions into one exact function. A general solution may represent infinitely many curves, but there is only one particular solution passing through a given point. Solutions may also have domain restrictions depending on the equation and the initial condition.
This lesson combines separation of variables with initial conditions. The process is: solve the differential equation generally, plug in the given initial condition, solve for the constant, and then write the resulting particular solution. This is important because many applied problems do not just ask for all possible solutions; they ask for the one that matches a real starting value or measured condition.