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## Homework Statement

x

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

## Homework Equations

y = x

^{r}

y' = r x

^{r-1}

y'' = r(r-1)x

^{r-2}

## The Attempt at a Solution

x

^{2}[r(r-1)x

^{r-2}] + x [r x

^{r-1}] + 4x

^{r}= 0

(r

^{2}-r)x

^{r}+ r x

^{r}+ 4x

^{r}= 0

[(r

^{2}-r) + r + 4]x

^{r}= 0

r

^{2}- r + r + 4 = 0

r

^{2}+ 4 = 0

from the quadratic equation i know that: r = 2i and r = -2i

so y = c

_{1}x

^{2i}+ c

_{2}x

^{-2i}

my question is how can i remove the imaginary number from the answer.

Thanks in advanced!