The given differential equation is a linear differential equation.

Integrating factor $=e^{\int \frac{2x}{1+x^2}dx}=1+x^2$
The solution of the differential equation is $y\left(1+x^2\right)=\int 3x^{2}dx=x^3+C$

$\because y\left(1\right)=1\Rightarrow C=1$
Hence, $y=f\left(x\right)=\frac{x^3+1}{x^2+1}$

So, $f\left(2\right)=\frac{9}{5}=1.8$