What’s with differential equation?
A differential equation is an equation that involves the derivatives of a function f as well as the function f itself. The equation is called a partial differential equation if partial derivatives are involved. In the case where only ordinary derivatives are present, the equation is then called an ordinary differential equation. If y = f(x) is a curve, then dy/dx is the slope of a tangent to the curve y at a point. So if dy/dx = 0 at point P, the tangent is parallel to x – axis because the slope of a tangent at point P is zero. This happens when y = f(x) = c, where c is a constant and a real number. More generally, for a function f where f(x) = c, dy/dx = 0. If dy/dx = infinity, then the slope of a tangent line is parallel to y – axis because it is equal to infinity or the slope