# Find the general solution to the homogeneous differential equation \frac { d ^ { 2 } y } { d t ^...

## Question:

Find the general solution to the homogeneous differential equation

{eq}\frac { d ^ { 2 } y } { d t ^ { 2 } } - 16 \frac { d y } { d t } + 164 y = 0. {/eq}

## Differential Equations:

The given differential equation is homogenous differential equation.

The solution of this equation will be of the following form if the roots of the characteristic equation are imaginary:

{eq}y=e^{ax}[c_{1}\cos bx+c_{2}\sin bx] {/eq}

## Answer and Explanation: 1

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View this answerWe are given the following equation

{eq}\dfrac { d ^ { 2 } y } { d t ^ { 2 } } - 16 \dfrac { d y } { d t } + 164 y = 0 {/eq}

We will now write the...

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Chapter 16 / Lesson 1Discover what separable differential equations are and their uses. Learn to identify if an equation is separable and how to solve them through given examples.