Toronto Math Forum
MAT2442018F => MAT244Lectures & Home Assignments => Topic started by: RubyZhan on December 05, 2018, 10:00:28 AM

Find the general solution of
$2x^2 y'' + 3xy'  y = 0$

Euler Suppose $y = x^r$
$\therefore$ $ y' = rx^{r1}$
$y'' = r(r1)x^{r2}$
$2x^2\cdot r(r1) X^{r2} + 3x \cdot rX^{r1}  X^r = 0$
$\therefore$ $X^r (r^2+3r + 2) = 0$
$\therefore$ $r^2 + 3r +2 =2 \qquad r = 2 \qquad r=1$
$\therefore$ $y = c_1 X^{1} + c_2 X^{2}$

Will Variation of Parameters method work??

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