Question

Solve the differential equation:
(x * y' - 1) * ln(x) = 2 * y

Answer 1

it's already been differentiated?

Answer 2

i dont understand what you mean.

Answer 3

nvm...do you know implicit differentiation?

Answer 4

yeah

Answer 5

ok that makes it easier...I'll calc it in a second

Answer 6

substituting \[x := e^t\] seems to make it a lot easier

Answer 7

the derivative of ln(x) is 1/x, but we have to do product rule

Answer 8

sorry man not sure on this one

Answer 9

and gotta get back studying for lin alg final -___-

Answer 10

try www.wolframalpha.com for an answer

Answer 11

oh ok thanks for your help :)
@ nowhereman: if i do that i get
y'*(e^t)*t=2y

Answer 12

I got \[(\frac{dy}{dt} - 1)t = 2y\]

Answer 13

assuming the function is analytic, that can be solved with power series

Answer 14

would i be able to have
\[(dy/dt) - (2/t)y=1\]
and then do an integrating factor:\[e^(intergral of (-2/t))\]?

Answer 15

no, I don't see how that would work.

Answer 16

... i dont understand what i should do then

Answer 17

umm and i dont get how you got the dt part

Answer 18

I used the chain rule \[\frac{dy}{dt} = \frac{dy}{dx}\frac{dx}{dt}\]