# Math Help - [SOLVED] Second order differential equations

1. ## [SOLVED] Second order differential equations

b)
Solve the initial value problem

y′′ + 2y′ + 5y = 0, y(0) = −2, y′(0) = 2

and write the final solution using real valued functions.

I did the question and got the answer to be Y = -2(e^x)cos2(x) is ithis right?

Help will be appreciated...thank you

2. Originally Posted by rajr
b)
Solve the initial value problem

y′′ + 2y′ + 5y = 0, y(0) = −2, y′(0) = 2

and write the final solution using real valued functions.

I did the question and got the answer to be Y = -2(e^x)cos2(x) is ithis right?

Help will be appreciated...thank you

So the auxillary equation is

$m^2+2m+5=0 \implies (m+1)^2+4=0 \implies m=-1 \pm 2i$

this tells us that our solution is of the form

$y=c_1e^{-x}\cos(2x)+c_2e^{-x}\sin(2x)$