Question

Find all the values of r such that y=Ax^r satisfies the equation:
y''+(x^-1)y'-y^3=0

Give a reason why other solutions must exist for this equation.

Answer 1

Hello estudier

Answer 2

That's an improvement on the previous version, lol

Answer 3

Hi..

Answer 4

I can get to
\[r(r-1)Ax^{r-2} + rAx^{r-2}-A^{3}x{3r}=0\]

Answer 5

By differentiating y=Ax^r and plugging in

Answer 6

Should be this actually
\[r(r-1)Ax^{r-2} + rAx^{r-2}-A^{3}x^{3r}=0\]

Answer 7

No one helped u...post it again.

Answer 8

Just that last bit, solve for r....

Answer 9

http://www.wolframalpha.com/input/?i=r*%28r-1%29*A*x^%28r-2%29+%2B+r*A*x^%28r-2%29-A^3*x^%283r%29+%3D+0%2C+for+r

if it's any help....