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

##### 1 Answer

Yes, Because of the Principle of Superposition

#### Explanation:

Yes the solutions

Why? Because of the Principle of Superposition

If it is known that the solutions **homogeneous** equation, and are linearly independent then from the Principle of Superposition

**homogeneous** equation.

So then it follows that if

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