The general solution of the equation `(dy)/(dx)=1+x y` is

Options

A. `y=ce^(-x^(2)//2)`
B. `y=ce^(x^(2)//2)`
C. `y=(x+c),e^(-x^(2)//2)`
D. None of these

Answer

D

Explanation

`(dy)/(dx)=1+xy`
or `(dy)/(dx)-xy=1`
I.F. `=e^(int-xdx)=e^(-x^(2)//2)`
Hence solution is `y.e^(-x^(2)//2) = inte^(-x^(2)+2)dx+c`.
`inte^(-x^(2)//2)dx` is not further integrable.