Transcription of Differential Equations - NCERT
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Differential Equations - NCERT
Differential EQUATIONS379 He who seeks for methods without having a definite problem in mindseeks for the most part in vain. D. HILBERT IntroductionIn Class XI and in Chapter 5 of the present book, wediscussed how to differentiate a given function f with respectto an independent variable, , how to find f (x) for a givenfunction f at each x in its domain of definition. Further, inthe chapter on Integral Calculus, we discussed how to finda function f whose derivative is the function g, which mayalso be formulated as follows:For a given function g, find a function f such thatdydx =g(x), where y = f(x) .. (1)An equation of the form (1) is known as a differentialequation. A formal definition will be given Equations arise in a variety of applications, may it be in Physics, Chemistry,Biology, Anthropology, Geology, Economics etc.
A differential equation involving derivatives of the dependent variable with respect to only one independent variable is called an ordinary differential equation, e.g., 2 3 2 2 d y dy dx dx + = 0 is an ordinary differential equation .... (5) Of course, there are differential equations involving derivatives with respect to
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