Let f '(x) = f (x), f (x) be a differentiable function, f (0) = 1, and f (x) = XF (x) + x ^ 2, find f' (x) and f (x)

Let f '(x) = f (x), f (x) be a differentiable function, f (0) = 1, and f (x) = XF (x) + x ^ 2, find f' (x) and f (x)

F(x)=xf(x)+x^2
F'(x)=f(x)+xf'(x)+2x
And f '(x) = f (x)
So, f (x) = f (x) + XF '(x) + 2x
F '(x) = - 2
Then: F (x) = - 2x + C
And f (0) = 1, that is, C = 1
So, f (x) = - 2x + 1, f '(x) = - 2