Solve the following differential equation (by regrouping terms)

[danny12345]

Homework Statement

(4x^3y^3-2xy)dx+(3x^4y^2-x^2)dy=0[/B]

Homework Equations

(4x^3y^3-2xy)dx+(3x^4y^2-x^2)dy=0

The Attempt at a Solution

i expanded it as 4x^3y^3dx-2xydx+3x^4y^2dy-x^2dy=0
next we have to take the common such that there will be
m(X)(xdy+ydx)[/B]
m(x) is the common onee

 

[epenguin]

If (without troubling to expand) you look at the numerical factors and the indices of the terms in the first expression they are an obvious ∂/∂x of something and if you look at the second expression, they are an obvious, not to give anything away...

 

[danny12345]

what that means?

 

[HallsofIvy]

If you really want to "regroup" then look at $$(4x^3y^3dx+ 3x^4y^2dy)- (2xydx+ x^2dy)$$.

 

[danny12345]

no i got it simply expand and make the common.common is not possible so we have to multiply it with some x^ny^n to the whole equation so we can make the common on(xdy+ydx) or(xdy-ydx).
multiply the expanded part by xy.
it becomes 4x^3y^4dx-2xy^2dx+3x^4y^3dy-x^2ydy=0
now -xy^2dx-xy^2dx-x^2ydy+3x^4y^3dy+4x^3y^4dx=0
=>-xy(ydx+xdy)-xy^2dx+3x^4y^3dy+3x^3y^4dx+x^3y^4dx=0
now it is very easy to do thnxx for your pateince

 

[epenguin]

what that means?

It means I couldn't say more without solving the problem for you which is not the policy for this forum.
It means that by policy I wouldn't say more unless you took the first step that I have indicated, after which something else would probably become obvious to you.
It means I think probably there is an explanation and another example of the same sort or same principle in the first two pages of the relevant chapter of your textbook.

Unless you are being asked to solve it a different way. I don't see that any regrouping is necessary.

 

[danny12345]

but the question asked for regrouping.the thing you are telling is not required in this question.

 

[Ray Vickson]

but the question asked for regrouping.the thing you are telling is not required in this question.

So, perform re-grouping if you want to. All you need to do is figure out how and why to re-group certain of the terms, and we are not allowed to help you any more with that. You need to do at least some of the work and show the results, and if you are still stuck you can ask for more hints.

 

[epenguin]

If you can solve the problem any which way it will help you anyway (and it's only a couple of lines) plus it might help you e.g. knowing the answer when we figure out what is they are wanting you to solve it.