In this question we will consider solutions to differential equations where y is a function of x. Throughout, a will always denote a constant. (a)

In this question we will consider solutions to differential equations where y is a function of x. Throughout, a will always denote a constant.

(a) What is the general solution to the equation y'= a?

(b) If y satisfies y' = 3 and y(2) = 5 what is y?

(c) What is the general solution to the equation y'' = a?

(d) If y satisfies y'' = 4, y'(1) = 5, and y(1) = 4, what is y?

(e) What is the general solution to the equation y''' = a?

(f) If y satisfies y'''= 6, y(0) = 0, y(1) = 1, and y(2) = 6 what is y?

Thanks a lot!