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 < λ1 < λ2 | Node | Unstable |
| λ1 < λ2 < 0 | Node | Asymptotically stable |
| λ1 < 0 < λ2 | Saddle Point | Unstable |
| 0 < λ1 = λ2 | Proper or improper node | Unstable |
| λ1 = λ2 < 0 | Proper or improper node | Asymptotically stable |
| λ1, λ2 = (0 < λ) ± iμ | Spiral Point | Unstable |
| λ1, λ2 = (λ < 0) ± iμ | Spiral Point | Asymptotically stable |
| λ1 = iμ, λ2 = -iμ | Center | Stable |
Equation Type
y'
y
| λ1 | = | ξ1 | = | ||
| λ2 | = | ξ2 | = |