December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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2.2 Separable Equations
INTRODUCTION
Consider the first-order equations dy/dx = f(x, y). When f does not depend on the variable y, that is, f(x, y) = g(x), the differential equation
(1)
can be solved by integration. If g(x) is a continuous function, then integrating both sides of (1) gives the solution y = ∫ g(x) dx = G(x) + c, where G(x) is an antiderivative (indefinite integral) of g(x). For example, if dy/dx = 1 + e2x, then y = ∫ (1 + e2x) dx or 
defined on (−, ).
A Definition
Equation (1), as well as its method of solution, is just a special ...
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