The solution of the differential equation `(e^(-2 sqrt(x))-(y)/(sqrt(x)))(dx)/(dy)=1` is given by

Options

A. `ye^(2sqrt(x))=x+c`
B. `ye^(-2sqrt(x))=sqrt(x)+c`
C. `y=sqrt(x)`
D. `y=3sqrt(x)`

Answer

A

Explanation

Given, differential equation can be rewritten as
`(dy)/(dx)+(y)/(sqrt(x))=e^(-2sqrt(x))`
Here, `P=(1)/(sqrt(x)), Q=e^(-2sqrt(x))`
`therefore IF =e^(int (1)/(sqrt(x))dx)=e^(2sqrt(x))`
`therefore` Solution is
`ye^(2sqrt(x))=int e^(2sqrt(x)) e^(-2sqrt(x))dx=int 1 dx`
`rArr ye^(2sqrt(x))=x+c`