Find the general solution of the homogeneous differential equation {eq}y'' + 1y = 0 {/eq}

## Question:

Find the general solution of the homogeneous differential equation {eq}y'' + 1y = 0 {/eq}

## Differential Equation: :

It is important to note that the general solution of the differential equation of the form: {eq}ay''+by'+cy=0 {/eq} is given by: {eq}y=e^{\alpha \:t}\left(c_1\cos \left(\beta \:t\right)+c_2\sin \left(\beta \:t\right)\right) {/eq} where {eq}k_1=\alpha +i\:\beta ,\:k_2=\alpha -i\:\beta \: {/eq} Also we have: {eq}y=e^{kt} {/eq}

## Answer and Explanation: 1

Become a Study.com member to unlock this answer! Create your account

View this answer

In the problem, we have to find the general solution of the homogeneous differential equation {eq}y'' + y =...

See full answer below.

#### Learn more about this topic:

from

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.