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 | 27th Feb, 2015, 05:22: PM

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 | 28th Feb, 2015, 11:17: AM

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