Question

one more help please. some difficult DEs which I can't figure out.

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

Answer 1

it is :

dx + (y^2 *x)dy = (x^2 *y) dy

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

any ideas on how to start lilMiss ??

Answer 6

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

Answer 7

just the same as what you did, i guess?

Answer 8

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

Answer 9

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

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

dx/dy = x^2y - y^2x

Answer 10

http://www.wolframalpha.com/input/?i=dx%2Fdy+%3D+x%5E2y+-+y%5E2x

i run into a gamma function at every turn :/

Answer 11

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

Answer 12

i think there is no closed form for that integral
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\[M\text{d}x+N\text{d}y=0\]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

Answer 13

no its not working

im wondering where these equations come from...this one and prev are very curious...

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

why? i'll try it in wolfram alpha

Answer 18

http://www.wolframalpha.com/input/?i=integrate++e%5E%28-x%5E3%29

Answer 19

:(

Answer 20

will i pass my midterm? :(

Answer 21

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

Answer 22

they were not normal

Answer 23

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. :)

Answer 24

welcome...:)