Practice question · Multiple choice
A separable differential equation and a non-separable one may describe equally simple business situations. What does separability actually reflect?
Hints
- Separability is about whether f(t,y) splits into g(t)h(y). Ask what that means about the process.
- Does an easy solution method imply simple behaviour? Consider the logistic equation.
Show the answer
D. That time and level can be factored apart in the model
Why
Separability is a convenience of form, not a claim about the dynamics, the logistic equation is separable and produces the whole S-curve. Option 4 overstates it too: many non-separable equations have closed forms, integrating factors being the standard route.
Practise First-Order Differential Equations
The app has 5 more questions on this lesson, and keeps your place in the course. Business I is free to start.
More questions on First-Order Differential Equations
- Sort these into growth models vs decay models.
- y = y0 e^kt solves doty = ky because the exponential is its own derivative up to a constant.
- At 7% continuous growth, the Rule of 70 says doubling time is roughly 70/7 = 10 years. Estimate e⁰.7.
- An exponential decay model stays accurate all the way down to the last few units of the quantity.
- Which spreadsheet formula computes continuous compound interest A = 1000 × e⁰.05 × 10?
- Half-life from a decay rate k is computed as ln 2 / |k| rather than 2/k. Why does a logarithm appear?
- Match each ODE to its economic model.