The equation of the curve satisfying the differential equation $y_2\left(x^2+1\right)=2x{y}_1$ passing through the point (0,1) and having slope of tangent at $x=0$ as 3 (where $y_2$ and $y_1$ represent 2nd and 1st order derivative), then (a)$y=f\left(x\right)$ is a strictly increasing function (b)$y=f\left(x\right)$ is a non-monotonic function (c)$y=f\left(x\right))$ has a three distinct real roots (d)$y=f\left(x\right)$ has only one negative root.

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