Final answer:
The correct method to find the general solution of a system of differential equations with a linearly dependent set is Variation of Parameters. It involves constructing particular solutions from the homogeneous equation's solution and combining them to form the general solution.
Step-by-step explanation:
To find the general solution of a system of differential equations with a linearly dependent set, the appropriate method to use would be C) Variation of Parameters. This technique allows us to find particular solutions for nonhomogeneous differential equations based on the general solution of the related homogeneous equation. Matrix inversion, separation of variables, and Laplace transform are other techniques for solving differential equations but are not specifically designed for systems with linearly dependent solutions.
In practice, one would first solve the associated homogeneous system to find the complementary solution. If the solutions are linearly dependent, it's necessary to use variation of parameters to construct a particular solution that considers the nonhomogeneity of the differential equations. The general solution is then the sum of the complementary and particular solutions.