# Are the particular integral and complementary function solutions of a Differential Equation linearly independent?

Yes, Because of the Principle of Superposition

Why? Because of the Principle of Superposition

Therefore it would be a solution of the homogeneous equation, and therefore it would not be the general solution of the non-homogeneous equation

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Yes, the particular integral and complementary function solutions of a linear homogeneous ordinary differential equation are linearly independent. This is a consequence of the principle of superposition, which states that the sum of any two solutions of a linear homogeneous differential equation is also a solution. As a result, the particular integral and complementary function solutions form a linearly independent set.

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