(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

y = x^{r}

y' = r x^{r-1}

y'' = (r^{2}-r)x^{r-2}

3. 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!

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# Homework Help: Help with Solving a Cauchy-Euler Differential Equation

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