Let `y=f(x)` be satisfying differential equation `e^(-x^(2))(dy)/(dx)=2xy^(2)` such that `f(0)=(1)/(2)`
Q. Which of the following statement is correct about `f(x)`?

Options

A. `f(x)` is unbounded
B. `f(x)` is bijective
C. `f(x)` is odd
D. None of these.

Answer

A

Explanation

`int(dy)/(y^(2))=int2xe^(x^(2))dx`
`-(1)/(y)=e^(x^(2))+C` point `(0.(1)/(2))` lies on the curve
`implies-2=1+C`
`impliesC=-3`
Hence `-(1)/(y)=e^(x^(2))-3`
`impliesf(x)=(1)/(3-e^(x^(2)))`
Hence, `f(x)` is even which means that it cannot be objective Also, denominator of `f(x)` becomes zero which implies that it cannot be bounded.