Final Review question

[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″