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.

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.

anonymous · Answer

Hello estudier

anonymous · Answer

That's an improvement on the previous version, lol

anonymous · Answer

Hi..

anonymous · Answer

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

anonymous · Answer

By differentiating y=Ax^r and plugging in

anonymous · Answer

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

anonymous · Answer

No one helped u...post it again.

anonymous · Answer

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

anonymous · Answer