# Clarification of a DE example

• Oct 23rd 2007, 04:46 PM
sixstringartist
Clarification of a DE example
My book states that:
$y'' +4y = 0$
has a general solution of:
$y(t) = c_1\cos {2t} + c_2\sin{2t}$

I dont see how they achieve this since the initial equation has a characteristic form of:
$r^2 + 4 = 0$
$r_{1,2} = \pm 2$
$\therefore$
$y(t) = c_1e^{2t} + c_2e^{-2t}$
• Oct 23rd 2007, 05:01 PM
Jhevon
Quote:

Originally Posted by sixstringartist
My book states that:
$y'' +4y = 0$
has a general solution of:
$y(t) = c_1\cos {2t} + c_2\sin{2t}$

I dont see how they achieve this since the initial equation has a characteristic form of:
$r^2 + 4 = 0$
$r_{1,2} = \pm 2$
$\therefore$
$y(t) = c_1e^{2t} + c_2e^{-2t}$

no, you solutions are not correct, we have complex solutions here. your solutions work for the difference of two squares, you have the sum of two squares here. use the quadratic formula
• Oct 23rd 2007, 05:29 PM
sixstringartist
Thank you. In my haste I was taking the sqrt of 4 and not -4. Thanks again.