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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 4th November 2016, 8:54 PM
Answered by 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

Answered by Expert 4th November 2016, 10:54 PM
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