← Differential Equations

How to solve

Substituting y = e^(rx) turns each derivative into a factor of r: y'' → r², y' → r, y → 1.

Steps

  1. y'' contributes r².
  2. p·y' contributes p·r.
  3. q·y contributes q; set the sum equal to zero.

Example

y'' − 5y' + 6y = 0. Characteristic equation?

  1. Substitute y = e^(rx).
  2. r² − 5r + 6 = 0.

Answer: r^2-5r+6=0

How to type answers

  • Type it like r^2-5r+6=0
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