First-order linear 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

   Solve $\dfrac{dy}{dx} + 2y = 8$ using an integrating factor. The general solution is $y = 4 + Ce^{-2x}$. Given $y(0) = 2$, find the constant $C$.

2. Warm-up

   Solve $\dfrac{dy}{dx} + 4y = 20$ using an integrating factor. The general solution is $y = 5 + Ce^{-4x}$. Given $y(0) = 3$, find the constant $C$.

3. Warm-up

   Solve $\dfrac{dy}{dx} + y = 4$ using an integrating factor. The general solution is $y = 4 + Ce^{-x}$. Given $y(0) = -6$, find the constant $C$.

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