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## Homework Statement

This is my first big differential equation that I have solved by myself, and I wanted to see if it is correct done, or what I have done wrong with it.

Would really appreciate if somebody could take a look on it.

y''+6y'+8y=0

when y(0)=1 and y'(0)=0

## The Attempt at a Solution

This is my solution

y''+6y'+8y=0

r

^{2}+6r+8=0

r=-3+- sqrt (9-8)= sqrt 1

r1= -2

r2= -4

y=Ce

^{-2x}+De

^{-4x}

y'=-2Ce

^{-2x}-4De

^{-4x}

y(0)=1 1=Ce

^{0}+De

^{0}=C+D

y'(0)=0 0=-2Ce

^{0}-4De

^{0}=-2C-4D

1=C+D

0=-2C-4D

I take 1=C+D and take -D on both sides so I get 1-D=C

I take 0=-2C-4D and take +2 on both sides so I get 2=C-4D

I now put in 1-D in it, and get 2=1-D-4D and that I can change to 3=-5D

I then take +5 on both sides and i get that 8=D

I go back to 1-D=C and I get that C=-7

I now take C and D and put them in the equation, so I get:

-7e

^{-2x}+8e

^{-4x}

Is this right, or have I made something wrong on the way?