class 12

Math

Calculus

Differential Equations

Let $y_{prime}(x)+y(x)g_{prime}(x)=g(x)g_{prime}(x),y(0)=0,x∈R,$ where $f_{prime}(x)$ denotes $dxdy(x) ,$ 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______

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