Which of the following differential equations are separable? (Select all that apply.)

A. $\displaystyle{\frac{dy}{dt} = t^2 - y^2 }$

B. $\displaystyle{\frac{dy}{dt} = t + 1 }$

C. $\displaystyle{\frac{dy}{dt} = ty-y }$

D. $\displaystyle{\frac{dy}{dt} = -3y }$

E. None of the above

Now consider the following equation. $$\int f'(x) \, dx = \int x \, dx$$ Which of the following functions $f(x)$ satisfy this equation? (Select all that apply.)

A. $f(x) = \frac{1}{2}x^2$

B. $f(x) = 7x^2$

C. $f(x) = x$

D. $f(x) = 7x$

E. $f(x) = x - 7$

F. $f(x)= \frac{1}{2}x^2 - 7$

G. $f(x) = x +7$

H. $f(x)= \frac{1}{2}x^2 + 7$

I. None of the above