Transcription of Differential Equations - NCERT
{{id}} {{{paragraph}}}
Example: biology
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. Hence, an indepth study of differentialequations has assumed prime importance in all modern scientific this chapter, we will study some basic concepts related to Differential equation,general and particular solutions of a Differential equation, formation of differentialequations, some methods to solve a first order - first degree Differential equation andsome applications of Differential Equations in different Basic ConceptsWe are already familiar with the Equations of the type:x
382 MATHEMATICS Example 1 Find the order and degree, if defined, of each of the following differential equations: (i) cos 0 dy x dx −= (ii) 2 2 2 0 d y dy dy xy x y dx dx dx ⎛⎞ + ⎜⎟−= ⎝⎠ (iii) yy e′′′ ++ =2 y′ 0 Solution (i) The highest order derivative present in the differential equation is
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: