first order linear diff equation

Question

some.random.cool.kid · Answer

shame its so sloppy i can barely read it.

anonymous · Answer

the answer should be y = x^3 + 2x^2 - x^-1

anonymous · Answer

my final equation was yx^-2 = 3x + c and it is so so far out from the real answer

luigi0210 · Answer

I would try getting y' by itself. so dividing everything by x^2:

$\Large y'+\frac{2}{x} y =x^2 +3x^{-2}$ 

Then find u(x) using P(x), 2/x:

$\Large u(x)= e^{\int \frac{2}{x}dx}=e^{2lnx} = x^2 $

Now multiply everything by u(x):

$\Large x^2 y' + 2xy=x^4+3$ 

Now use the reverse product rule: 

$ \Large (x^2*y)'=x^4+3$ 

Make sense so far? >.<

anonymous · Answer

yes yes.. thank you so much

luigi0210 · Answer

Is that what you got? I think I might of done something wrong

anonymous · Answer

be cause in the orig eq.. its -2xy

luigi0210 · Answer

Ohhh, I didn't see that negative.. that completely messes everything up.. sorry :P 

So it should be: 

$\Large x^{-2}y' - 2 x^{-3}y = 1+3 x^{-4} $ 

$\Large (x^{-2} *y)'  = 1+3x^{-4} $ 

Then we just integrate and it should get us the general equation..

anonymous · Answer

thank you so muuuucccch =)

luigi0210 · Answer

No problem :P

Can you handle the rest or do you need more help?

anonymous · Answer

i think i can do this. haha thank you

luigi0210 · Answer

Alright, if you ever need help just call xD

And I'm actually just learning this stuff too so I was lucky to be able to make sense :P

anonymous · Answer

=) sure

luigi0210 · Answer

Sure to what? To needing more help? o.O