If integrating factor of `x(1-x^2)dy+(2x^2y-y-a x^3)dx=0` is `e^(intp dx ,)` then `P` is equal to

Options

A. `(2x^(2)-ax^(2))/(x(1-x^(2))`
B. `2x^(3)-1`
C. `(2x^(2)-a)/(ax^(3))`
D. `(2x^(2)-1)/(x(1-x^(2))`

Answer

D

Explanation

`x(1-x^(2))dy+(2x^(2)-y-ax^(3))dx=0`
or `x(1-x^(2))(dy)/(dx)+2x^(2)y-y-ax^(3)=0`
or `x(1-x^(2))(dy)/(dx) + y(2x^(2)-1)=ax^(3)`
or `(dy)/(dx) + (2x^(2)-1)/(x(1-x^(2))y)=(ax^(3))/(x(1-x^(2))`
Which is of the form `(dy)/(dx) + Py=Q`
Its integrating factor is `e^(intPdx)`
Here, `P=(2x^(2)-1)/(x(1-x^(2))`