emilykaiser9700 emilykaiser9700
  • 15-10-2021
  • Mathematics
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Solve the homogeneous linear ordinary differential equation y’’’+3y’’-4y’-12y=0

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LammettHash
LammettHash LammettHash
  • 15-10-2021

The ODE,

y''' + 3y'' - 4y' - 12y = 0

has characteristic equation

r ³ + 3r ² - 4r - 12 = 0

which can be factorized as

r ² (r + 3) - 4 (r + 3) = (r ² - 4) (r + 3) = 0

so that its roots are r = ±2 and r = -3.

Then the characteristic solution to the ODE is

y(x) = C₁ e ⁻²ˣ + C₂ e ²ˣ + C₃ e ⁻³ˣ

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