Differential Equations

Slope Field Generator for First-Order ODEs

Visualize dy/dx = f(x,y) as a direction field: short marks at each grid point colored by slope sign. Overlay a gold solution curve through any initial condition.

Live Calculator Â· Direction Field Â· Differential Equations

Inputs

dy/dx = f(x, y)

x window [min, max]

y window [min, max]

Initial Condition xâ‚€

Initial Condition yâ‚€ = y(xâ‚€)

Result

ODE

dy/dx = y

Initial Condition

y(0) = 1

Color Key

â– Positive slope â– Negative slope â– Zero slope

Solution Curve

Gold curve computed via Euler's method (h=0.05), forward and backward from IC.

Interpretation

Draw the slope field above.

Slope Field + Solution Curve