Linear second-order DEs ay'' + by' + cy = 0. Solve the characteristic equation am² + bm + c = 0 — three cases by discriminant.
Three cases
- Two real roots m₁, m₂ → y = C₁e^(m₁x) + C₂e^(m₂x).
- Repeated root m → y = (C₁ + C₂x)e^(mx).
- Complex roots α ± βi → y = e^(αx)(C₁ cos βx + C₂ sin βx).