## anonymous 3 years ago one more help please. some difficult DEs which I can't figure out. dx + (y^2x)dy = (x^2 y) dy

1. anonymous

it is : dx + (y^2 *x)dy = (x^2 *y) dy

2. amistre64

i wonder: $\frac{dx}{dy}+xy^2=x^2y$ $x^{-2}x'+y^2x^{-1}=y$ $z=x^{-1}:~z^{-1}=x;~z^{2}=x^{-2};~-z^{-2}z'=x';~$ $z^2(-z^{-2}z')+y^2z=y$ $-z'+y^2z=y$ $z'-y^2z=-y$ justwondering, i got no idea if its right tho

3. amistre64

$e^{-\frac{1}{3}y^3}z'-y^2e^{-\frac{1}{3}y^3}z=-ye^{-\frac{1}{3}y^3}$ $e^{-\frac{1}{3}y^3}z=-\int ye^{-\frac{1}{3}y^3}dy$ $z=-~e^{\frac{1}{3}y^3}\int ye^{-\frac{1}{3}y^3}dy$

4. amistre64

i doubt that was right; unless we were spose to go into the Gamma function :/

5. amistre64

any ideas on how to start lilMiss ??

6. anonymous

sorry. poor internet connection here. well, what i was thinking was to get the integrating factor of the equation.

7. anonymous

just the same as what you did, i guess?

8. amistre64

the twp dys have me iffy; i have never had to deal with them in that state

9. amistre64

dx + (y^2x)dy = (x^2 y) dy dx = (x^2y - y^2x)dy dx/dy = x^2y - y^2x

10. amistre64

http://www.wolframalpha.com/input/?i=dx%2Fdy+%3D+x%5E2y+-+y%5E2x i run into a gamma function at every turn :/

11. anonymous

help! integrate this please. : int. e^(-1/3 *y^3)dy

12. anonymous

i think there is no closed form for that integral ---------------------------------------------------------------------- $M\text{d}x+N\text{d}y=0$another method is multiplynig by $$x^a.y^b$$ and searching for $$a$$ and $$b$$ for which$\frac{\partial (x^a.y^b.M)}{\partial y}=\frac{\partial (x^a.y^b.N)}{\partial x}$which turnes the equation to an exact diff equation let me try it

13. anonymous

no its not working im wondering where these equations come from...this one and prev are very curious...

14. anonymous

i already got this one, using bernoulli's equation with respect to x, are you familiar wit that? my only problem is how am i going to integrate e^(-1/3 *y^3)dy

15. anonymous

$\large \int e^{-\frac{y^3}{3}} dy$?

16. anonymous

but there is no closed form for this integral...

17. anonymous

why? i'll try it in wolfram alpha

18. anonymous
19. anonymous

:(

20. anonymous

will i pass my midterm? :(

21. anonymous

sure u will...dont think of these 2 prev problems

22. anonymous

they were not normal

23. anonymous

aw. thank you so much. really really thank you for everything that you've done just so i could have answers. one medal isn't enough, i guess. :)

24. anonymous

welcome...:)