SOLUTION

$y(x,\alpha) - x - \alpha f (y(x,\alpha))=0$ .

$\frac{\partial y}{\partial x} - 1 - \alpha \frac{\partial f}{\partial y} \frac{\partial y}{\partial x} = 0 \Longleftrightarrow \frac{\partial y}{\partial x} \Big{[} 1 - \alpha f'(y) \Big{]} = 1$ .

$\frac{\partial y}{\partial \alpha} - f(y(x,\alpha)) - \alpha \frac{\partial f}{\partial y} \frac{\partial y}{\partial \alpha} = 0 \Longleftrightarrow \frac{\partial y}{\partial \alpha} \Big{[} 1 - \alpha f'(y) \Big{]} = f(y)$ .

$\Longrightarrow \frac{\partial y}{\partial \alpha} = f(y) \frac{\partial y}{\partal x}$ .