Introduction to Differential Equation

Differential Equations

1. Type

Ordinary Differential Equations

ex ) y" + y' = 0 , y" + 7 x( y' ) ^3 = 3x , ...

Partial Differential Equations

ex )

, ...

2. Linearity

Linear Differential Equations 

ex) y" + xy' = 7x,  8y"' + 3y' = xy, ...

Nonlinear Differential Equations

ex) (y"")^19 + (y")^ 30 - xy = 30x, ...

3. Order

1st, 2nd, 3rd, ... , n-th Order Differential Equations

ex)

y' + y^3 = 0 -> 1st order differential equation

(x^50)y" + (y')^300 + y = x -> 2nd order differential equation

x(y"')^20 + y = 3x^398 -> 3rd order differential equation