Math, asked by sipun2k2, 5 months ago

The general solution of dy/dx +xy=x is ??​

Answers

Answered by senboni123456
0

Step-by-step explanation:

We have,

 \frac{dy}{dx}   + xy=x  \\

I.F. =  {e}^{    \int xdx}  =   {e}^{ \frac{ {x}^{2} }{2} }  \\

So, solution is,

 {e}^{ \frac{ {x}^{2} }{2} } .y =  \int \: x. {e}^{ \frac{ {x}^{2} }{2} } dx \\

  \implies {e}^{ \frac{ {x}^{2} }{2} } .y =  {e}^{ \frac{ {x}^{2} }{2} } + C \\

  \implies y = 1 + C{e}^{ -  \frac{ {x}^{2} }{2} }  \\

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