CBSE Class 12-science Answered

$S o l v e space t h e space f o l l o w i n g space d i f f e r e n t i a l space e q u a t i o n colon y minus x fraction numerator d y over denominator d x end fraction equals 3 open parentheses 1 plus x squared fraction numerator d y over denominator d x end fraction close parentheses$ Please provide solution to this question

Asked by Topperlearning User | 04 Nov, 2016, 08:54: PM

Expert Answer

$y minus x fraction numerator d y over denominator d x end fraction equals 3 open parentheses 1 plus x squared fraction numerator d y over denominator d x end fraction close parentheses rightwards double arrow y minus 3 equals x fraction numerator d y over denominator d x end fraction plus 3 x squared fraction numerator d y over denominator d x end fraction rightwards double arrow y minus 3 equals left parenthesis 3 x squared plus x right parenthesis fraction numerator d y over denominator d x end fraction rightwards double arrow fraction numerator d y over denominator y minus 3 end fraction equals fraction numerator d x over denominator 3 x squared plus x end fraction rightwards double arrow integral fraction numerator d y over denominator y minus 3 end fraction equals integral fraction numerator d x over denominator 3 x squared plus x end fraction rightwards double arrow log open vertical bar y minus 3 close vertical bar equals 1 third integral fraction numerator d x over denominator open parentheses x plus begin display style 1 over 6 end style close parentheses squared minus begin display style 1 over 36 end style end fraction rightwards double arrow log open vertical bar y minus 3 close vertical bar equals 1 third open parentheses 6 over 2 log open vertical bar fraction numerator x plus begin display style 1 over 6 end style minus 1 over 6 over denominator x plus 1 over 6 plus 1 over 6 end fraction close vertical bar close parentheses plus log C rightwards double arrow log open vertical bar y minus 3 close vertical bar equals log open vertical bar fraction numerator 3 x over denominator 3 x plus 1 end fraction close vertical bar plus log C rightwards double arrow y minus 3 equals fraction numerator 3 x C over denominator 3 x plus 1 end fraction rightwards double arrow left parenthesis y minus 3 right parenthesis left parenthesis 3 x plus 1 right parenthesis equals x C to the power of apostrophe space w h e r e space C to the power of apostrophe equals 3 C space i s space t h e space r e q u i r e d space d i f f e r e n t i a l space e q u a t i o n$