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CBSE Class 12-science Answered

In each of the following examples verify that the given function is a solution of the corresponding  differntial equation. 
Asked by aadeshpdabre | 24 May, 2016, 11:00: AM
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1. space C o n s i d e r space t h e space e q u a t i o n comma space y equals c subscript 1 sin x plus c subscript 2 cos x space space space... left parenthesis 1 right parenthesis D i f f e r e n t i a t i n g space t h e space a b o v e space e q u a t i o n comma space w e space h a v e comma fraction numerator d y over denominator d x end fraction equals c subscript 1 cos x minus c subscript 2 sin x space space space... left parenthesis 2 right parenthesis D i f f e r e n t i a t i n g space o n c e space a g a i n space w i t h space r e s p e c t space t o space x comma space w e space h a v e comma fraction numerator d squared y over denominator d x squared end fraction equals negative c subscript 1 sin x plus c subscript 2 cos x space space space space.... left parenthesis 3 right parenthesis A d d i n g space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 3 right parenthesis comma space w e space h a v e comma fraction numerator d squared y over denominator d x squared end fraction plus y equals c subscript 1 sin x minus c subscript 2 c o s x minus c subscript 1 sin x plus c subscript 2 cos x rightwards double arrow fraction numerator d squared y over denominator d x squared end fraction plus y equals 0 2. G i v e n space t h a t space y space cross times s e c x equals tan x plus c D i f f e r e n t i a t i n g space t h e space a b o v e space e q u a t i o n comma space w e space h a v e comma fraction numerator d y over denominator d x end fraction cross times s e c x plus y s e c x cross times tan x equals s e c squared x D i v i d i n g space t h e space e q u a t i o n space b y space s e c x comma space w e space h a v e comma fraction numerator d y over denominator d x end fraction plus y cross times t a n x equals s e c x 3. G i v e n space t h a t space x y equals log y plus c D i f f e r e n t i a t i n g space t h e space a b o v e space e q u a t i o n comma space w e space h a v e comma fraction numerator d y over denominator d x end fraction cross times x plus y equals 1 over y fraction numerator d y over denominator d x end fraction rightwards double arrow fraction numerator d y over denominator d x end fraction cross times x minus 1 over y fraction numerator d y over denominator d x end fraction equals negative y rightwards double arrow 1 over y fraction numerator d y over denominator d x end fraction minus fraction numerator d y over denominator d x end fraction cross times x equals y rightwards double arrow fraction numerator 1 minus x y over denominator y end fraction cross times fraction numerator d y over denominator d x end fraction equals y rightwards double arrow open parentheses 1 minus x y close parentheses cross times fraction numerator d y over denominator d x end fraction equals y squared rightwards double arrow fraction numerator d y over denominator d x end fraction equals fraction numerator y squared over denominator open parentheses 1 minus x y close parentheses end fraction
Answered by Vimala | 24 May, 2016, 05:42: PM

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CBSE 12-science - Maths
the question is given in the attachment in case the attachment is not appearing i have mentioned this question: Solve the differential equation yexydx=⎛⎜⎝xexy+y2⎞⎟⎠ dy. (toppr.com) in this question they have solved the differential equation by substituting v = x/y, but as of my knowledge, this substitution can be made only for zero order homogeneous differential equations, yet the answer they got is correct and is verified by calculator, so does this mean that we can appl this substitution to any differential equation? PS: in some sites they have solved this question by other methods and they have specified substituting v = x/y wont work here as this is not a homogenous differential equation. So can you clarify what is the correct way to solve this question, THANK YOU!
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CBSE 12-science - Maths
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sir i only need the correct option
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Define differential equation.
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Define the order of a differential equation.
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Find the order and degree of the differential equation: .
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