Question

# The graph of y = f(x) contains the point (0,2), \frac{dy}{dx}=\frac{-x}{ye^{x^2}}, and f(x) is greater than 0 for all x, then f(x)= A) 3+e^{-x^2} B) \sqrt{3}+e^{-x} C) 1+e^{-x} D) \sqrt{3+e^{-x^2}} E) \sqrt{3+e^{x^2}}

Functions
The graph of y = f(x) contains the point (0,2), $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{-{x}}}{{{y}{e}^{{{x}^{{2}}}}}}}$$, and f(x) is greater than 0 for all x, then f(x)=
A) $$\displaystyle{3}+{e}^{{-{x}^{{2}}}}$$
B) $$\displaystyle\sqrt{{{3}}}+{e}^{{-{x}}}$$
C) $$\displaystyle{1}+{e}^{{-{x}}}$$
D) $$\displaystyle\sqrt{{{3}+{e}^{{-{x}^{{2}}}}}}$$
E) $$\displaystyle\sqrt{{{3}+{e}^{{{x}^{{2}}}}}}$$