Answer: A general solution of a differential equation is a solution that contains all possible solutions of the equation, including all arbitrary constants. It provides a general form of the solution that can be customized to fit the specific conditions of the problem.
For example, the general solution of a second-order linear homogeneous differential equation of the form
y'' + p(x)y' + q(x)y = 0
is a combination of two linearly independent functions, often represented by y = c1y1(x) + c2y2(x), where c1 and c2 are arbitrary constants and y1(x) and y2(x) are two linearly independent solutions of the differential equation.
The general solution represents the most general form of the solution that takes into account all possible solutions, including all arbitrary constants. To find a specific solution, one must apply initial or boundary conditions to determine the values of the arbitrary constants.
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