Choose the solutions for the differential equation. Select all that apply.
$$3x^{2}y"+6xy'-6y=0$$
$$y=e^{}$$$$y=x^{3}$$$$y=e^{-x}$$$$y=-2y^{-3}$$

Question

Choose the solutions for the differential equation. Select all that apply.
$$3x^{2}y"+6xy'-6y=0$$
$$y=e^{}$$$$y=x^{3}$$$$y=e^{-x}$$$$y=-2y^{-3}$$

kkutie7 · Answer

* first one is $$y=e^{x}$$

kkutie7 · Answer

* last one
$$y=x^{-2}$$

kkutie7 · Answer

also did this, but it hasn't helped me
$$y=e^{x}\rightarrow y'=e^{x}\rightarrow y"=e^{x}$$
$$y=x^{3}\rightarrow y'=3x^{2}\rightarrow y"=6x$$
$$y=e^{-x}\rightarrow y'=-e^{-x}\rightarrow y"=e^{x}$$
$$y=x^{-2}\rightarrow y'=-2x^{-3}\rightarrow y"=6x^{-4}$$

surana · Answer

@Nnesha ? Could you help, please?

kkutie7 · Answer

@pooja195 do you know how to do this?

kkutie7 · Answer

@zepdrix help?

kkutie7 · Answer

@hero?

zepdrix · Answer

Why didn't taking derivatives help you? :o
Hmm

kkutie7 · Answer

Well none of them were a solution so I guess I goofed, but I'm not sure how

zepdrix · Answer

Oh hmm :)
$$\large\rm 3x^2y''+6xy'-6y$$

zepdrix · Answer

Your derivatives look correct, so that's a good start.
Maybe just input one of them incorrectly, hmm.

kkutie7 · Answer

I guess I'll rewrite them to see if I get it right.

zepdrix · Answer

Ooo I think I see a solution :)
I won't spoil the fun though, while you're typing hehe

kkutie7 · Answer

$$3x^{2}e^{x}+6xe^{x}-6e^{x}=0$$
$$3x^{2}(6x)+6x*3x^{2}-6x^{3}=0$$
$$3x^{2}e^{-x}-6xe^{-x}-6e^{-x}=0$$
$$3x^{2}6x^{-4}+6x(-2x^{-3})-6x^{-2}=0$$
is this written right?

zepdrix · Answer

Hmm ya those look correct :)

kkutie7 · Answer

smh the last one is a solution isn't it

zepdrix · Answer

yayyy \c:/

kkutie7 · Answer

lol thanks for the help. now I have to go and do more =/

zepdrix · Answer

:D