How to find parametric curve from differential equations

Question

How would you find the parametric curve for this set of parametric differential equations: $$x'=\frac{1}{y},y'=2xy$$ I tried dividing the second equation by the first and treating it as a normal differential equation. However, this results in a normal cartesian equation which can have multiple parametric representations, some of which don't satisfy the equations. How can I solve these equations while preserving their parametric nature?

Answer 1

$$x''=-\dfrac {y'}{y^2}=-\dfrac {2x}y$$ $$x''=-2xx'$$ $$x''=-(x^2)'$$ Integrate. $$x'=-x^2+C$$ This is separable.