Multiple choice

The solution to the ordinary differential equation $\frac{d^2y}{dx^2} + \frac{dy}{dx} - 6y = 0$is

  1. y = $c_1e^{3x} + c_2e^{-2x}$
  2. y = $c_1e^{3x} + c_2e^{2x}$
  3. y = $c_1e^{-3x} + c_2e^{2x}$
  4. y = $c_1e^{-3x} + c_2e^{-2x}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The characteristic equation is r^2 + r - 6 = 0. Factoring gives (r + 3)(r - 2) = 0, so roots are r = -3 and r = 2. The general solution is y = c1 * e^(-3x) + c2 * e^(2x).