Solve the initial value problem: `y-x(dy)/(dx)=2(1+x^2(dy)/(dx)),\ y(1)=1`

Explanation

$$ \begin{aligned} &y-x \frac{d y}{d x}=2+2 x^{2} \frac{d y}{d x} \\ &\therefore y-2=\left(2 x^{2}+x\right) \frac{d y}{d x} \\ &\therefore \frac{1}{2 x^{2}+x} \cdot d x=\int \frac{1}{y-2} d y \end{aligned} $$
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