Answer
See the explanation below.
Work Step by Step
(a) A solution can be defined for a function $y=f(x)$ that satisfies the first-order differential equation $\dfrac{dy}{dx}=k(x,y)$. In order to do that, the function $f(x)$ and its first-order derivative must be substituted into that equation.
The general solution of an nth order differential equation includes $n$ arbitrary constants. After simplification, the solution of the first-order differential equation $k(x,y)=\dfrac{dy}{dx}$ attains one arbitrary constant.
(b) A particular solution of a differential equation can be found by assigning specific values to the arbitrary constants that satisfy the conditions, such as the Initial-Value Problem, or Boundary Conditions, depending on the order of the differential equation.
