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CBSE Class 12-science Answered

in differential equation of linear differential equation . after variable separation method. while integrating we use constant C but i have seen in many of the question they have taken the constant as log C. how do we get to know where to take constant C or where to take it as log C.


if you are unable to understand my question check ncert solutions of exercise 9.5 question no. 6 and 2. in question 2 we have used constant C but in question 6 we have used Log C

Asked by rohit dalal | 27 Feb, 2015, 05:22: PM
answered-by-expert Expert Answer
F o r space c o n s tan t s comma space i t space d o e s space n o t space m a t t e r comma space i f space y o u space p u t space C space o r space log space C. L o g a r i t h m i c space c o n s tan t s space a r e space u s e d space t o space s i m p l i f y space t h e space c a l c u l a t i o n s. I f space t h e r e space a r e space log a r i t h m s space o n space b o t h space t h e space s i d e space o f space t h e space e q u a t i o n comma t h a t space i s space log space y space equals f open parentheses log space x close parentheses comma space t h e n space w e space p u t space log a r i t h m i c space c o n s tan t comma space log space C I f space t h e space s o l u t i o n space o f space t h e space d i f f e r e n t i a l space e q u a t i o n space i s space o f space t h e space f o r m comma y equals f left parenthesis log space x right parenthesis comma space t h e n space w e space p u t comma space s i m p l y space C. T h e space v a l u e space o f space C space c h a n g e s space a c c o r d i n g l y. I space h o p e space y o u space u n d e r s tan d factorial factorial factorial
Answered by Vimala Ramamurthy | 28 Feb, 2015, 11:17: AM

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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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Asked by ashwinskrishna2006 | 24 Dec, 2023, 04:59: PM
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CBSE 12-science - Maths
dy/dx+2xy=e-x2
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Asked by rishavgautam705 | 26 Nov, 2023, 01:55: PM
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CBSE 12-science - Maths
find the particular solution
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Asked by pranavmishra1108 | 17 Sep, 2023, 11:12: AM
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CBSE 12-science - Maths
Please refer to the uploaded image for the doubt.
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Asked by arjunsah797 | 22 May, 2022, 10:25: AM
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CBSE 12-science - Maths
Solve: 𝑦 𝑑𝑦 = (𝑦 2 − 1)(𝑥 + 1) 𝑑𝑥.
Asked by arunabhapaul123 | 25 Jan, 2022, 02:13: PM
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CBSE 12-science - Maths
the solution
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CBSE 12-science - Maths
sir i only need the correct option
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CBSE 12-science - Maths
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