Calculus Textbook Voice-over Sample
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Vocal Characteristics
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EnglishVoice Age
Young Adult (18-35)Accents
North American (General)Transcript
Note: Transcripts are generated using speech recognition software and may contain errors.
Chapter six Differential Equations, Section 6.1 Slow Fields and You'll Er's Method General and Particular Solutions and this text. You will learn that the physical phenomenon can be described by differential equations. Recall that a differential equation in X and Y is an equation that involves X Y and derivatives of why, for example, two X y prime minus three y equals zero is a differential equation. And Section 6.2, you will see that problems involving radioactive decay, population growth and Newton's law of cooling can be formulated in terms of differential equations. As a function y equals F of X is called a solution off a differential equation. If the equation is satisfied, win why and its derivatives are replaced by F of X and its derivatives, for example, differentiation and substitution would show that why equals e to the negative. Two X is a solution of the differential equation. Why Prime plus two y equals zero. It could be shown that every solution of this differential equation is a form of why equals c e to the negative two X where C is any real number. The solution is called the General solution. Some differential equations have singular solutions that cannot be written as special cases of the general solution. Such solutions, however, are not considered in this text. The order of differential equation is determined by the highest order derivative and the equation. For instance, why Prime equals four y is a first order differential equation in section 4.1 example nine. You saw how the second order differential equation s double prime of T equals 32 has the general solution as of t equals negative 16 t squared plus C to the one times t plus C to the to, which contains two arbitrary constants. It can be shown that a differential equation of order n has a general solution within arbitrary constants.