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Vector Algebra

Question
CBSEENMA12033062
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Solve:
dy over dx space equals space fraction numerator straight x left parenthesis 2 space log space straight x space plus space 1 right parenthesis over denominator sin space straight y space plus space straight y space cosy end fraction

Solution

The given differential equation is
            dy over dx space equals space fraction numerator straight x left parenthesis 2 space log space straight x space plus space 1 right parenthesis over denominator sin space straight y space plus space straight y space cosy end fraction
Separating the variables, we get,
                                   left parenthesis sin space straight y space plus space straight y space cosy right parenthesis space dy space equals space straight x left parenthesis 2 space logx space plus 1 right parenthesis space dx
therefore space space space space integral left parenthesis sin space straight y space plus straight y space cos right parenthesis space dy space equals space integral straight x space left parenthesis 2 space log space straight x space plus 1 right parenthesis space dx therefore space space space integral sin space ydy space plus space integral straight y space cosy space dy space equals space 2 space integral logx. space straight x space dx space plus space integral straight x space dx therefore space space space space space space space minus cosy space plus space straight y space siny space minus space integral 1. space sin space straight y space dy space equals space 2 open square brackets left parenthesis log space straight x right parenthesis. space straight x squared over 2 minus integral 1 over straight x. straight x squared over 2 dx plus straight x squared over 2 close square brackets therefore space space space minus cosy space plus space ysiny space space plus space cosy space space equals space straight x squared logx minus straight x squared over 2 plus straight x squared over 2 plus straight c therefore space space space straight y space sin space straight y space equals space straight x squared space logx space plus straight c space which space is space required space equation.

Some More Questions From Vector Algebra Chapter

Determine order and degree (if defined) of differential equations:
y' + y = ex

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