Observe and solve.

Calculus Level 4

Let \(\displaystyle y'(x)+y(x)g'(x)=g(x)g'(x) ,\quad y(0)=0 \) where x is real no. , \(f'(x)\) denotes \(\frac{df(x)}{dx} \) and \(g(x)\) is a given non constant differentiable function on \(R\) with \(g(0)= g(2) = 0\). Then the value of \(y(2)\) is

This problem is a part of the set advanced is basic
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