Differential equation: an equation containing derivatives of an unknown function.
Ordinary differential equation (ODE): an equation that contains one or several derivatives of an unknown function.
Partial differential equations (PDEs): differential equations that involve partial derivaties of an unknown functino of two or more variables.
order n: nth derivative of the unknown function y is the highest derivative of y in the equation
implicit form: F(x,y,y’) = 0
explicit form: y’ = f(x,y)
y’ = f(x,y)가 주어지면 각 x, y에 해당하는 slope을 plot할 수 있는데, 이를 direction field (or slope field)라고 한다. direction field가 유용한 이유는 ODE를 풀지 않고도 solution이 대략 어떻게 생겼는지 알 수 있기 때문이다. 이 성질을 이용한 것이 바로 Euler’s method 이다.