A particular solution is a specific set of values for the variables in a general solution that satisfies a given equation or system of equations. It is a unique solution that fulfills all the conditions of the problem.
A general solution contains variables and constants, while a particular solution has specific values for those variables and constants. A general solution may have an infinite number of particular solutions.
To find a particular solution using substitution, replace the variables in the general solution with the given values and solve for the remaining variable. The resulting solution will be a particular solution that satisfies the given equation.
Yes, a particular solution can be a complex number. In cases where the given equation involves complex numbers, the particular solution must also be a complex number in order to satisfy the equation.
Finding particular solutions is important because it allows us to find specific values that satisfy a given equation or system of equations. These solutions can be used to solve real-world problems and make predictions in various fields such as physics, engineering, and economics.