Multiple choice

The solution of the ordinary differential equation $\frac{dy}{dx} + 2y$= 0 for the boundary condition, y = 5 at x = 1 is

  1. y = e - 2x

  2. y = 2e - 2x

  3. y = 10.95 e - 2x

  4. y = 36.95 e - 2x

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The differential equation dy/dx + 2y = 0 has the general solution y = C * e^(-2x). Using the boundary condition y(1) = 5, we get 5 = C * e^(-2), so C = 5 * e^2. Thus, y = 5 * e^2 * e^(-2x) = 5 * e^(2 - 2x). 5 * e^2 is approximately 36.95.