Ordinary Differential Equations

Equations, wherein the unknown quantity is a function rather than a variable and involves derivatives of the unknown function, are known as differential equations. An ordinary differential equation is a special case where the unknown function has only one independent variable with respect to which derivatives occur in the equation. If, on the other hand, derivatives of more than one variable occur in the equation, then it is known as a partial differential equation, and that is the topic of Chapter 11 . This chapter focuses on ordinary differential equations (ODEs) and explores symbolic and numerical methods for solving this type of equation. Analytical closed-form solutions to ODEs often do not exist. But for certain special kinds of ODEs, there are analytical solutions, and in those cases, there is a chance that we can find solutions using symbolic methods. If that fails, we must, as usual, resort to numerical techniques.