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CBSE Class 12-science Answered

solve given differential equations  1. space space space space space y minus x fraction numerator d y over denominator d x end fraction equals a left parenthesis y squared plus fraction numerator d y over denominator d x end fraction right parenthesis

2. space space space space space space fraction numerator d y over denominator d x end fraction equals sin left parenthesis x plus y right parenthesis plus cos left parenthesis x plus y right parenthesis
Asked by Eng.surinder.singh | 25 Jan, 2019, 12:56: PM
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Only one question per posting is solved
 
begin mathsize 16px style y space minus space x fraction numerator d y over denominator d x end fraction space equals space a y squared plus a fraction numerator d y over denominator d x end fraction
y left parenthesis 1 minus a y right parenthesis space equals space left parenthesis a plus x right parenthesis fraction numerator d y over denominator d x end fraction
fraction numerator d y over denominator y left parenthesis 1 minus a y right parenthesis end fraction equals fraction numerator d x over denominator a plus x end fraction
b y space w r i t i n g space t h e space L H S space a s space p a r t i a l space f r a c t i o n space colon space fraction numerator d y over denominator y end fraction plus fraction numerator a d y over denominator left parenthesis 1 minus a y right parenthesis end fraction space equals space fraction numerator d x over denominator a plus x end fraction
B y space i n t e g r a t i n g space t h e space a b o v e space e x p r e s s i o n colon space log space y space minus space a space log space left parenthesis 1 minus a y right parenthesis space equals space log space left parenthesis a plus x right parenthesis

log open parentheses y over open parentheses 1 space minus space a y close parentheses to the power of a close parentheses space equals space log open parentheses fraction numerator 1 over denominator open parentheses a plus x close parentheses end fraction close parentheses plus log space C space space semicolon space w h e r e space log space C space i s space c o n s tan t space o f space i n t e g r a t i o n
h e n c e space y over open parentheses 1 space minus space a y close parentheses to the power of a space equals space fraction numerator C over denominator open parentheses a plus x close parentheses end fraction end style
Answered by Thiyagarajan K | 26 Jan, 2019, 12:08: PM
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