Differential Equations Workbook For Dummies®

Chapter 4. Working with Linear Second Order Differential Equations

In This Chapter

• Solving second order differential equations that are both linear and homogeneous

• Reveling in the three roots: real, distinct roots; complex roots; and real, identical roots

Are linear second order differential equations keeping you up at night? You know the ones. They look like this:

y″ + p(x)y′ + q(x)y = g(x)

where

and

Then this is the chapter for you because it's all about practicing solving linear second order differential equations that are also homogeneous.

Note: In this chapter, you only solve differential equations for regions where p(x), q(x), and g(x) are continuous functions (that is, where they don't take quick jumps in value). Usually there will be an initial condition, such as

y(x_o) = y_o

and

y′(x_o) = y_o′