ABSTRACT
In this chapter, we explored ways of solving higher order differential equations with constant coefficients. The characteristic equation is used to formulate the solution to the homogeneous differential equation while the concept of the Wronskian introduced in Chapter 3 is invoked to get the particular solution. The difficulties encountered in using the roots of the characteristic equation of the higher order differential equations is clearly articulated in terms of the relationships that might exist among the various roots making it difficult to proceed as the order increases beyond 4. As has been done throughout, the solution obtained through the use of roots and the Wronskian is compared to the one obtained using the theory of Laplace transforms. Additional confirmation is provided through the use of numerical techniques based on the Runge-Kutta method in Matlab. Differential equations with orders larger than the 4th are solved using Laplace transforms and results are compared using the Runge-Kutta method.
