Find the general solution of the homogeneous differential equation {eq}y'' -4y' + 4y = 0 {/eq}

Question:

Find the general solution of the homogeneous differential equation {eq}y'' -4y' + 4y = 0 {/eq}

Differential equation:

The process of finding a derivative is called differentiation. The given differential equation is a homogeneous differential equation

To solve this problem, we'll take the trial solution {eq}y= Ae^{mx} {/eq}, to get the auxiliary equation. Next, we'll solve the quadratic equation to get the desired solution.

Answer and Explanation: 1

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We are given: {eq}\displaystyle{y}'' - 4{y}' + 4y =0 {/eq}

If the trial solution is taken as {eq}y= Ae^{mx} {/eq} , the auxiliary equation...

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Differential Calculus: Definition & Applications

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Chapter 13 / Lesson 6
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This lesson explores differential calculus. It defines a differential and delves into the many uses of differential equations.


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