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Equations wherein the unknown quantity is a function, rather than a variable, and that involve derivatives of the unknown function, are known as differential equations. An ordinary differential equation is the 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. Here we focus on ordinary differential equations (in the following abbreviated as ODEs), and we explore both symbolic and numerical methods for solving this type of equations in this chapter. Analytical closed-form solutions to ODEs often do not exist, but for many special types 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.
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- Ordinary Differential Equations
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- Chapter 9