# Finding the solution to the initial value problem

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• Apr 21st 2014, 09:10 PM
crownvicman
Finding the solution to the initial value problem
The equation is y"+8y'+25y=0 with y(0)= 2 & y'(0)=0

I calculated the general solution and figured out the motion is Underdamped. I can't seem to figure out the solution to the initial value problem.

I found S1 and S2 to be equal -4 +/- 3i ad the Ygen = (k1)^(-4t)cost(t) + i(k2)e^(-4t)sin(t)
• Apr 21st 2014, 09:27 PM
SlipEternal
Re: Finding the solution to the initial value problem
• Apr 22nd 2014, 10:59 AM
HallsofIvy
Re: Finding the solution to the initial value problem
Quote:

Originally Posted by crownvicman
The equation is y"+8y'+25y=0 with y(0)= 2 & y'(0)=0

I calculated the general solution and figured out the motion is Underdamped. I can't seem to figure out the solution to the initial value problem.

I found S1 and S2 to be equal -4 +/- 3i ad the Ygen = (k1)^(-4t)cost(t) + i(k2)e^(-4t)sin(t)

That "(k1)^{-4t}", I presume, is a typo. But you also forgot the "3" in "-4+ 3i". The general solution is \$\displaystyle Ygen= k1 e^{-4t}cos(3t)+ k2 e^{-4t}sin(3t)\$ (I have absorbed the "i" into k2).

Then \$\displaystyle Ygen(0)= k1e^0 cos(0)+ k2 e^0 sin(0)= k1= 2\$.

Differentiate Ygen and set that derivative, at x= 0, equal to 0 to find k2.
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