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Unformatted text preview: Problem (Final Exam 2009). Solve the following Bernoulli differential equation: (2 + x 2 ) dy dx + xy = x 3 y 3 . Explanation to the statement of the problem. : Solve means find all functions y = y ( x ) satisfying the above (differential) equation. Here y is dependent variable, x is independent variable hence y = y ( x ) is function of x . Also, dy dx (Leibnitz notation for a derivative) is the (first) derivative of y with respect to x that is denoted also by y or y ( x ) (Newton notation for (first) derivative). Hence, the problem can be formulated in the following form, by using Newtons notation of a derivative: Problem (Final Exam 2009). Solve the following Bernoulli differential equation: (2 + x 2 ) y + xy = x 3 y 3 . Solution. (1) Taking into account that dy dx = y ( x ) = y Leibnitz and Newton notation of a derivative the given differential equation can written as (2 + x 2 ) y + xy = x 3 y 3 ....
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This note was uploaded on 03/28/2010 for the course ENGR 213 taught by Professor Nicolassullivan during the Spring '09 term at York UK.
- Spring '09