Question

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

Answer 1

Step-by-step explanation:

We have,

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

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

So, solution is,

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

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

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