Solve the differential equation y" - 4y' + 4y = e^{-2t} + sin2t.

Question:

Solve the differential equation

y" - 4y' + 4y = {eq}e^{-2t} {/eq} + sin2t.

Differential Equation:

The general function of a differential equation consists of a complimentary and a particular solution.

A particular solution can be obtained by assigning specific values to the arbitrary constants. The complementary solution is the only solution to the homogeneous differential equation. We are after a solution to the non homogeneous differential equation wherein the initial conditions must satisfy that solution instead of the complementary solution.

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Given the Differential equation y" - 4y' + 4y = {eq}e^{-2t}+\sin (2t) {/eq}

The operator form is {eq}(D^{2}-4D+4)t=e^{-2t}+sin(2t) {/eq} where...

First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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In this lesson you'll learn how to solve a first-order linear differential equation. We first define what such an equation is, and then we give the algorithm for solving one of that form. Specific examples follow the more general description of the method.