8. Topic 8(COLON) Differential Equations

Lesson 8.1: First-order Separable Differential Equations — Quiz

Test your understanding of lesson 8.1: first-order separable differential equations with 5 practice questions.

Practice Questions

Question 1

What is the general solution to the first-order separable differential equation $\frac{dy}{dx} = 3y$?

Question 2

For the equation $\frac{dy}{dx} = -4y$, what is the particular solution if $y(0) = 5$?

Question 3

What is the equilibrium solution for the differential equation $\frac{dy}{dt} = 2 - y$?

Question 4

If the separation of variables leads to $\frac{dy}{y} = 6dx$, what is the first step in solving the differential equation?

Question 5

What final form do we get when we solve the separable equation $\frac{dy}{dx} = 2y^2$ using the initial condition $y(1) = 1$?