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Final Review question

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**RubyZhan**:

Find the general solution of

$2x^2 y'' + 3xy' - y = 0$

**Meiyi Lu**:

Euler Suppose $y = x^r$

$\therefore$ $ y' = rx^{r-1}$

$y'' = r(r-1)x^{r-2}$

$2x^2\cdot r(r-1) X^{r-2} + 3x \cdot rX^{r-1} - X^r = 0$

$\therefore$ $X^r (r^2+3r + 2) = 0$

$\therefore$ $r^2 + 3r +2 =2 \qquad r = -2 \qquad r=-1$

$\therefore$ $y = c_1 X^{-1} + c_2 X^{-2}$

**Zhihao Zuo**:

Will Variation of Parameters method work??

**ansleyliu**:

I think better stick with Euler since there's 2x^2 in front of 𝑦″

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