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Solve the differential equation

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

Answer and Explanation: 1

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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...

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First-Order Linear Differential Equations

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Chapter 16 / Lesson 3
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Learn to define what a linear differential equation and a first-order linear equation are. Learn how to solve the linear differential equation. See examples.


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