The integrating factor of `x(dy)/(dx)+(1+x)y=x `is

Options

A. x
B. 2x
C. `e^( x log x)`
D. `ex^(x)`

Answer

D

Explanation

`x(dy)/(dx)+(1+x)y=x`
`implies(dy)/(dx)+(1+x)/(x)y=1`
If `=e^(int^(1+x)/(x)dx)=e^(int^(dx)/(x)+intdx)`
`=e^(logx+x)=xe^(x)`