Differential equations quiz

Five questions on Differential equations. Answer all 5 to see your score.

0 of 5 answered

Question 1 of 5

A 90°C cup of coffee sits in a 70°C room. Newton's law of cooling says the temperature changes at a rate proportional to the difference between the coffee and the room. Which ODE models the coffee temperature T(t), with k > 0?

Question 2 of 5

Sketching the direction field for \frac{dP}{dt} = P(2 - P), what can you conclude about the equilibrium solutions P = 0 and P = 2?

Question 3 of 5

Solve the separable initial-value problem \frac{dy}{dx} = y^2 e^x with y(0) = 1.

Question 4 of 5

Use an integrating factor to solve \frac{dy}{dx} + 2y = e^{-2x}. What is the general solution?

Question 5 of 5

For the logistic population model \frac{dP}{dt} = 0.5 P \left(1 - \frac{P}{100}\right), at what population does P grow fastest, and what is the carrying capacity?

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