Slope fields can be used to visualize the solutions of a first order differential equation of the form \[ \frac{dy}{dx} = f(x,y) \] where \(y\) is a function of \(x\).

At any point \((x,y)\) in the Cartesian plane, the value of \(\frac{dy}{dx} = f(x,y)\) gives us the slope of the tangent line to the graph of the differential equation's solution.

By drawing short line segments with that slope at several points, we can begin to see the "shape" of the solutions of the differential equation.

Enter a differential equation in the form \(y'=f(x,y)\), and the slope field will update automatically. Decrease the spacing for shorter, denser line segments, or increase for longer segments.

If you want to display a specific solution to the differential equation, enter a condition \(y(x_0)=y_0\) or double click on the graph to change the initial value point. The solution passing through the point \((x_0,y_0)\), if it can be computed via Euler's method, will be displayed.

Use the slider below the graph to zoom in or out. Click and drag the graph to reposition.

This applet was created using JavaScript, the math.js library, and the Konva graphics library.