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)

Re: Finding the solution to the initial value problem

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 (I have absorbed the "i" into k2).

Then .

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