# Find the general solution for: D^2y+10Dy+25y=0

## Question:

Find the general solution for: {eq}D^2y+10Dy+25y=0 {/eq}

## Differential Equation in Calculus:

If the second order differential equation is of the form:{eq}D^2y+P_{1}Dy +P_{2}y=0 {/eq}, we'll take the trial solution {eq}y= Ae^{mx} {/eq}, to get the auxiliary equation.

We need to find out the value of {eq}m {/eq} in order to get the desired solution.

## Answer and Explanation:

{eq}D^2y+10Dy+25y=0 {/eq}

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

{eq}m^2+10m+25=0 {/eq}

{eq}\...

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Differential Calculus: Definition & Applications

from Calculus: Help and Review

Chapter 13 / Lesson 6
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