Baldirri Baldirri

09-10-2021
Mathematics

contestada

Find the general solution of the given higher-order differential equation. y''' − 7y'' + 8y' + 16y = 0

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LammettHash LammettHash

09-10-2021

The ODE

y''' - 7y'' + 8y' + 16y = 0

has characteristic equation

r ³ - 7r ² + 8r + 16 = 0

which can be factorized as

(r - 4)² (r + 1) = 0

Then the characteristic solution to the ODE is

y(x) = C₁ e ⁴ˣ + C₂ x e ⁴ˣ + C₃ e ⁻ˣ

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