Let y(x) be the solution of the differential equation `(xlogx)(dy)/(dx)+y=2xlogx, (xge1)`, Then y(e) is equal to

Options

A. e
B. 0
C. 2
D. 2e

Answer

d

Explanation

Given , differential equation is
` (x log x) (dy)/(dx) + y = 2x log x, (x ge 1)`
` rArr (dy)/(dx) +y/(x log x) = 2 `
This is a linear differential equation .
` :. If = e^(int 1/(x log x)dx) = e ^(log (log x)) log x `
Now, the solution of given differential equation is given by
` y * log x = int log x* 2 dx `
` rArr y * log x = 2 [ x log x - x ] +C`
At x = 1, C = 2
`rArr y* log x = 2 [ x log x - x ] +2`
At `x = e , y = 2 (e - e) +2`
` rArr y = 2`