## anonymous 5 years ago Solve the differential equation: (x * y' - 1) * ln(x) = 2 * y

1. anonymous

2. anonymous

i dont understand what you mean.

3. anonymous

nvm...do you know implicit differentiation?

4. anonymous

yeah

5. anonymous

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

6. nowhereman

substituting $x := e^t$ seems to make it a lot easier

7. anonymous

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

8. anonymous

sorry man not sure on this one

9. anonymous

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

10. anonymous

11. anonymous

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

12. nowhereman

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

13. nowhereman

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

14. anonymous

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

15. nowhereman

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

16. anonymous

... i dont understand what i should do then

17. anonymous

umm and i dont get how you got the dt part

18. nowhereman

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