AP Calculus AB: Separation of Variables — Drill 1

About This Drill

AP Calculus AB: Separation of Variables — Drill 1 is a Math practice drill covering Separation of Variables. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice solving separable differential equations by separating variables, integrating both sides, and applying initial conditions to find particular solutions. These AP Calculus AB skills appear on both the multiple-choice and free-response sections of the exam.

Questions in This Drill

1. Which of the following differential equations is not separable?
2. If \( \dfrac{dy}{dx} = 2xy \) and \( y > 0 \), which of the following is the general solution?
3. Consider the differential equation \( \dfrac{dy}{dx} = \dfrac{3x^2}{y} \) with initial condition \( y(0) = 4 \). What is the particular solution?
4. A student solves the separable equation \( \dfrac{dy}{dx} = \dfrac{x}{y} \) with initial condition \( y(0) = -3 \) and obtains \( y = -\sqrt{x^2 + 9} \). Which of the following best explains why the negative square root is chosen rather than the positive square root?
5. The differential equation \( \dfrac{dy}{dx} = \dfrac{2x+1}{3y^2} \) has the initial condition \( y(1) = 2 \). What is the value of \( y(0) \)?