The general solution of the given higher-order differential equation. y''' − 7y'' + 8y' + 16y = 0 is known to be y(x) = C₁ e ⁴ˣ + C₂ x e ⁴ˣ + C₃ e ⁻ˣ
A differential equation is known to be seen as any equation that has one or a lot of terms and the derivatives of one given variable with the view of the other variable.
Note that from the question;
y''' - 7y'' + 8y' + 16y = 0
So the characteristics of the equation
r ³ - 7r ² + 8r + 16 = 0
This can be factorized to be:
(r - 4)² (r + 1) = 0
Therefore, the characteristic solution to the question above is:
y(x) = C₁ e ⁴ˣ + C₂ x e ⁴ˣ + C₃ e ⁻ˣ
Therefore, The general solution of the given higher-order differential equation. y''' − 7y'' + 8y' + 16y = 0 is known to be y(x) = C₁ e ⁴ˣ + C₂ x e ⁴ˣ + C₃ e ⁻ˣ
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Find the general solution of the given higher-order differential equation. y''' − 7y'' + 8y' + 16y = 0
