Differential equations

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   The function $y = 2e^{-2x}$ is proposed as a solution of the differential equation $\dfrac{dy}{dx} = -2y$. Differentiate $y$ to confirm that it satisfies the equation, then find the value of $\dfrac{dy}{dx}$ at $x = 0$. Round to 3 decimal places.

2. Warm-up

   The function $y = 4e^{3x}$ is proposed as a solution of the differential equation $\dfrac{dy}{dx} = 3y$. Differentiate $y$ to confirm that it satisfies the equation, then find the value of $\dfrac{dy}{dx}$ at $x = 1$. Round to 3 decimal places.

3. Warm-up

   The function $y = 4e^{-3x}$ is proposed as a solution of the differential equation $\dfrac{dy}{dx} = -3y$. Differentiate $y$ to confirm that it satisfies the equation, then find the value of $\dfrac{dy}{dx}$ at $x = 1$. Round to 3 decimal places.

Problems shown under their original terms: Generated (template, solver-computed).