Ordinary Differential Equation

Definition

An equation that contains one or several derivatives of unknown functions

Types

• Linear ODE
  • Homogeneous Linear ODE
  • Non-Homegeneous Linear ODE
• Non-linear ODE

Facts

Initial Value Problem

Definition

ODE $F(x,y,y^{\prime })=0$ or $y^{\prime }=G(x,y)$ with an initial condition $y(x_0)=y_0$

Facts

The general solution of an ODE is a family of infinitely many solution curves

The solution curve of an IVP sould pass through the given point $(x_0,y_0)$

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