Answer
See answer below.
Work Step by Step
a) A solution is a function $y=f(x)$ that satisfies the first-order differential equation $f(x,y)=\dfrac{dy}{dx}$ when the function $f(x)$ and its first-order derivative are plugged into the equation.
A general solution of an nth order differential equation involves $n$ arbitrary constants. A solution of the first-order differential equation $f(x,y)=\dfrac{dy}{dx}$ has one arbitrary constant after simplification.
b) A particular solution of a differential equation is a solution which can be obtained from the general solution by assigning specific values to the arbitrary constants and satisfies the conditions for determining the values of the arbitrary constants, which can be obtained in the form of an Initial-Value Problem, or Boundary Conditions, depending on the order of differential equation.
