1st order ODE

Before you see this post,

see

e ( mathematical constant )

Relationship between Integral and Differential

Exact Differential Equation

There is a formula of ODE like former.

We can express the formula like latter.

We can consider 2 conditions.

First, the formula is non-exact differential equation.

Second, it is exact differential equation.

If it's non-exact differential equation, we can put F(x,y) and multiply with it. 

Let's suppose F(x,y) = F(x) , x dependent function.

We can find what function y is.

Exact Differential Equation

Before you see this post,

see

Relationship between Integral and Differential

Total differential

Definition of exact differential equation

Solutions of exact differential equation

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