The complete solution (or complete integral) of linear differential equations involves the complementary function + particular integral, which corresponds to the second option:

Complementary function + particular integral.

This is because:

1. The complementary function is the solution of the homogeneous differential equation (when the right-hand side equals zero).
2. The particular integral is the specific solution for the non-homogeneous part of the equation (when the right-hand side is non-zero).

Would you like me to explain this in more detail or solve an example related to this concept?

Related Questions:

1. What is the method to find the complementary function for a linear differential equation?
2. How is the particular integral calculated for linear equations with constant coefficients?
3. What is the difference between definite and indefinite integrals in solving differential equations?
4. Why do linear differential equations require both complementary and particular solutions?
5. Can you explain the role of initial conditions in determining the constants in the complete solution?

Tip:

Always check if the differential equation is homogeneous or non-homogeneous before starting your solution, as