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 $(x_0,y_0)$