# 2D Differential Equation Grapher

This simulator lets you experiment with a two-dimensional constant-coefficient ordinary differential equation system.

You can click an example case from the list, or enter a custom equation, and the vector field will be graphed below. This is not a phase portrait; the arrow lengths accurately represent the velocity. The dashed green lines are the eigenvectors. Click on the graph to place a ball and it will follow the differential equation, leaving a trail behind to show the trajectory!

Eigenvalues | Critical Point (0,0) | Stability |

0 < λ_{1} < λ_{2} | Node | Unstable |

λ_{1} < λ_{2} < 0 | Node | Asymptotically stable |

λ_{1} < 0 < λ_{2} | Saddle Point | Unstable |

0 < λ_{1} = λ_{2} | Proper or improper node | Unstable |

λ_{1} = λ_{2} < 0 | Proper or improper node | Asymptotically stable |

λ_{1}, λ_{2} = (0 < λ) ± iμ | Spiral Point | Unstable |

λ_{1}, λ_{2} = (λ < 0) ± iμ | Spiral Point | Asymptotically stable |

λ_{1} = iμ, λ_{2} = -iμ | Center | Stable |

__Equation Type__

y'

y

λ_{1} | = | ξ_{1} | = | ||

λ_{2} | = | ξ_{2} | = |