What is the solution of the differential equation $\dfrac{\mathrm{dy} }{\mathrm{d} x}=\dfrac{x}{y}$, with the initial condition, at $x=0, y=1?$

1. $x^{2}=y^{2}+1$
2. $y^{2}=x^{2}+1$
3. $y^{2}=2x^{2}+1$
4. $x^{2}-y^{2}=0$