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## Homework Statement

x

^{2}y'' + x y' + 4 y = 0

## Homework Equations

y = x

^{r}

y' = r x

^{r-1}

y'' = (r

^{2}-r)x

^{r-2}

## The Attempt at a Solution

x

^{2}{(r

^{2}-r)x

^{r-1}} + x{r x

^{r-1}} + 4x

^{r}

r

^{2}- r + r + 4

r

^{2}+ 4 = 0

r = +- 2i

y = C

_{1}x

^{2i}+ c

_{2}x

^{-2i}

My question is how can i remove the imaginary number with cos[] and sin[]

If you could be as descriptive as possible i'd really appreciate it!

Thanks in advanced!