STEMORIA scientific instrument

Differential Equation Explorer

Explore dy/dt = ky through its analytic solution, local rate, graph, and linked state.

Mathematics

Manipulate

Measure

Interpret

Linked scientific model

Differential Equation Explorer

Explore the first-order equation dy/dt = ky through its analytic exponential solution and local rate.

I2 · equation-driven modelone state · synchronized views

Primary scientific view

Solution curve

live model output

Interactive measurement plotMove across the graph to inspect values

y(t)

y (dimensionless) vs time (arbitrary unit)

Active point · time (arbitrary unit) 2 · y (dimensionless) 2.226

ODE

dy/dt = ky

y(t) = y₀eᵏᵗ

Data

y(t)

2.2255

dy/dt

0.89022

Doubling time

1.7329

Interpretation

Predict before testing

What does a negative k produce when y₀ is positive?

STEMORIA scientific instrument

Differential Equation Explorer

Explore dy/dt = ky through its analytic solution, local rate, graph, and linked state.

Mathematics

Manipulate

Measure

Interpret

Linked scientific model

Differential Equation Explorer

Explore the first-order equation dy/dt = ky through its analytic exponential solution and local rate.

I2 · equation-driven modelone state · synchronized views

Primary scientific view

Solution curve

live model output

Interactive measurement plotMove across the graph to inspect values

y(t)

y (dimensionless) vs time (arbitrary unit)

Active point · time (arbitrary unit) 2 · y (dimensionless) 2.226

ODE

dy/dt = ky

y(t) = y₀eᵏᵗ

Data

y(t)

2.2255

dy/dt

0.89022

Doubling time

1.7329

Interpretation

Predict before testing

What does a negative k produce when y₀ is positive?