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

1. lilMissMindset Group Title

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

2. amistre64 Group Title

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 Group Title

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

4. amistre64 Group Title

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

5. amistre64 Group Title

any ideas on how to start lilMiss ??

6. lilMissMindset Group Title

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

7. lilMissMindset Group Title

just the same as what you did, i guess?

8. amistre64 Group Title

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

9. amistre64 Group Title

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

10. amistre64 Group Title

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

11. lilMissMindset Group Title

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

12. mukushla Group Title

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 Group Title

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

14. lilMissMindset Group Title

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 Group Title

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

16. mukushla Group Title

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

17. lilMissMindset Group Title

why? i'll try it in wolfram alpha

18. mukushla Group Title
19. lilMissMindset Group Title

:(

20. lilMissMindset Group Title

will i pass my midterm? :(

21. mukushla Group Title

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

22. mukushla Group Title

they were not normal

23. lilMissMindset Group Title

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 Group Title

welcome...:)