Solve `x dy=(y+x(f(y/x))/(f^(prime)(y/x)))dx`

The solution of differential equation y y^(prime)=x((y^2)/(x^2)+(f((y^2)/(x^2)))/(f^(prime)((y^2)/(x^2)))) is

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Let f: R->R be a differentiable function with f(0)=1 and satisfying the equation f(x+y)=f(x)f^(prime)(y)+f^(prime)(x)f(y) for all x ,\ y in R . Then, the value of (log)_e(f(4)) is _______

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