In the earlier section we looked at first order differential equations. In this section we will move on to second order differential equations. Just as we did in the previous section we will see some particular cases of second order differential equations which we can solve. Unlike the previous section though, we are going to have to be even more limiting as to the types of differential equations which we'll look at. It will be needed in order for us to in fact be capable to solve them.
Now there is a list of topics which will be covered in this section.
Basic Concepts- Some of the fundamental concepts and ideas that are included in solving second order differential equations.
Real Roots- Solving differential equations whose feature equation has real roots
Complex Roots- Solving differential equations whose feature equation complex real roots.
Repeated Roots- Solving differential equations whose feature equation has repeated roots.
Reduction of Order- A brief see the topic of reduction of order. It will be one of the few times in this section that non-constant coefficient differential equation will be looked at.
Fundamental Sets of Solutions- A look at several of the theory behind the solution to second order differential equations, comprising looks at the Wronskian and basic sets of solutions.
More on the Wronskian- An application of the Wronskian and an optional method for finding it.
Nonhomogeneous Differential Equations- A rapid look in how to solve nonhomogeneous differential equations in general.
Undetermined Coefficients- The primary method for solving nonhomogeneous differential equations which we'll be looking at in this section.
Variation of Parameters- The other method for solving nonhomogeneous differential equations.
Mechanical Vibrations - This is an application of second order differential equations. In this section we focuses on mechanical vibrations, even a simple change of notation can shift this in almost any other engineering field.