Let `y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R ,` where `f^(prime)(x)` denotes `(dy(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______

Explanation

To solve the differential equation given by

\[ y'(x) + y(x) g'(x) = g(x) g'(x) \]

with the conditions \( g(0) = 0 \) and \( g(2) = 0 \), we will follow these steps:

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