Find the general solution to y′′+6y′+13y=0. Give your answer as y= In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2.

Step-by-step explanation:

In order to find the general solution of a homogeneous second order differential equation, we need to solve the characteristic equation. This is basically as easy as solving a quadratic.

For a second order differential equation of type:

Has characteristic equation:

Whose solutions are the roots from which the general solution can be formed. There are three cases:

Real roots:

Repeated roots:

Complex roots:

Therefore:

The characteristic equation for:

Is:

Solving for :

So:

Hence, the general solution of the differential equation will be given by:

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step-by-step explanation:

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