### Author Topic: Final Review question  (Read 2170 times)

#### RubyZhan

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##### Final Review question
« on: December 05, 2018, 10:00:28 AM »
Find the general solution of
$2x^2 y'' + 3xy' - y = 0$

#### Meiyi Lu

• Jr. Member
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##### Re: Final Review question
« Reply #1 on: December 05, 2018, 10:11:58 AM »
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

• Jr. Member
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##### Re: Final Review question
« Reply #2 on: December 11, 2018, 10:51:18 AM »
Will Variation of Parameters method work??

#### ansleyliu

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##### Re: Final Review question
« Reply #3 on: December 11, 2018, 01:26:12 PM »
I think better stick with Euler since there's 2x^2 in front of 𝑦″