The solution of the differential equation `(dy)/(dx)=(x+y)/x` satisfying the condition `y""(1)""=""1` is

Options

A. ` y = x log x +x`
B. ` y = log x +x`
C. ` y = x log x+x^(2)`
D. ` y = xe^(x-1)`

Answer

a

Explanation

Given equation cn be writtn as
` (dy)/(dx)-1/x*y = 1`
` :. If = ^(-f 1/x dx) = e ^(-logx) =1/x `
`:. ` Required solution is
` y (1/x) = int 1/x dx+ C = log x + C`
Since , y (1) =1
` rArr C = 1`
` :. Y = x log x +x`