- #1
itunescape
- 11
- 0
Homework Statement
y" + 2y' + 10y=0
y(0)=1
y'(0)= -1
solve initial value problem
Homework Equations
e^( ~ + iu)t= e^ ~t (cos ut + i sin ut)
The Attempt at a Solution
i've gotten pretty far into the problem, but i just can't seem to get the correct final answer.
I changed y" + 2y' + 10y=0 int r^2 +2r +10= 0 and used the quadratic formula to get:
r= 1-3i and r= 1+ 3i
so for the general solution i got:
yg= y1 + y2
yg= c1e^t( cos 3t + i sin 3t) + c2e^t( cos 3t - i sin 3t)
i need to solve for the constants:
y= c1 e^t cos 3t + c2 i sin3t ( an example in the book followed this method but i don't know why there is a c2 next to sin 3t and why there isn't a y2 )
i got c1= 1 and took the derivative to find c2 and got c2= -2/3
y'= c1 e^t cos 3t -3c1e^t sin 3t + c2e^tsin3t + 3 cos3tc2e^t
overall i got yg= 2e^tcos 3t but the answer is suppose to be yg= e^-t cos 3t. why? the textbook i use has this annoying ability of skipping 90% of the arithmatic work within examples, so I'm not sure where I could have gone wrong, can u guys help? :/