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Solve the following problem. {y}'' - 2y' - 8y = 0

Question:

Solve the following problem.

{eq}{y}'' - 2y' - 8y = 0 {/eq}

Answer and Explanation:

{eq}{y}'' - 2y' - 8y = 0 {/eq}

Auxiliary equation,

{eq}t^2-2t-8=0 \\ (t-4)(t+2)=0 \\ t-4=0, t+2=0 \\ t=-2,4 {/eq}

{eq}y(x) = c_{1}e^{-2x} +c_{2}e^{4x} {/eq}


Learn more about this topic:

First-Order Linear Differential Equations

from GRE Math: Study Guide & Test Prep

Chapter 16 / Lesson 3
637

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