## lilMissMindset 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. lilMissMindset

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. lilMissMindset

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

7. lilMissMindset

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. lilMissMindset

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

12. mukushla

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. mukushla

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

14. lilMissMindset

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. mukushla

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

16. mukushla

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

17. lilMissMindset

why? i'll try it in wolfram alpha

18. mukushla
19. lilMissMindset

:(

20. lilMissMindset

will i pass my midterm? :(

21. mukushla

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

22. mukushla

they were not normal

23. lilMissMindset

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. mukushla

welcome...:)