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A differential equation (de) is an equation involving a function and its deriva-tives. Differential equations are called partial differential equations (pde) or or-dinary differential equations (ode) according to whether or not they contain partial derivatives. The order of a differential equation is the highest order derivative occurring.
used textbook “Elementary differential equations and boundary value problems” by Boyce & DiPrima (John Wiley & Sons, Inc., Seventh Edition, c 2001). Many of the examples presented in these notes may be found in this book. The material of Chapter 7 is adapted from the textbook “Nonlinear dynamics and chaos” by Steven
show particular techniques to solve particular types of rst order di erential equations. The techniques were developed in the eighteen and nineteen centuries and the equations include linear equations, separable equations, Euler homogeneous equations, and exact equations. Soon this way of studying di erential equations reached a dead end.
SECTION 1.3 presents a geometric method for dealing with differential equations that has been known for a very long time, but has become particularly useful and important with the proliferation of readily
Readers are familiar with solving algebraic equations. For example, the solu-tions to the quadratic equation x2 −x= 0 are easily found to be x= 0 and x= 1, which are numbers. An ordinary differ-ential equation, or just differential equation, is another type of equation where the unknown is not a number, but a function. We call the unknown ...
A complete survey course in differential equations for engineering and science can be constructed from the lectures and examples, by skipping the technical details supplied in the text.
LINEAR DIFFERENTIAL EQUATIONS. first-order linear differential equation is one that can be put into the form. dy. dx. P x y. Q x. where P and Q are continuous functions on a given interval. This type of equation occurs frequently in various sciences, as we will see.