Nonlinear nonexact first order ODE

Hey

How can I solve

dy/dx = (3x^2 * y + y^2) / (2x^3 + 3xy)

Hopefully you can understand that. It is clearly nonlinear. It is also nonexact and I cannot find an integrating factor that works. I also tried y=vx to no avail. Can someone help me out with this and point me in the right direction?

Thanks

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Re: Nonlinear nonexact first order ODE

Find g(x,y) to make diff eq exact:

Then solution is:

for c=1,2,3,....16

http://mathhelpforum.com/attachment....1&d=1349835058

also check out:

Re: Nonlinear nonexact first order ODE

How is that supposed to help? I am not familiar with diagrams like these for differential equations at all

Re: Nonlinear nonexact first order ODE

Hi MaxJasper !

There is a mistake in your first line (permutation of dx and dy).

Hi Shanter !

Your differential equation is solvable, but very arduously (too difficult to an home work).

I suspect that there is a "-" missing in the wording :

If the equation was : dy/dx = - (3x^2 * y + y^2) / (2x^3 + 3xy) then the integrating factor would be easy to find and the result : (x^3)(y^2)+(y^3)x = C

2 Attachment(s)

Re: Nonlinear nonexact first order ODE

Re: Nonlinear nonexact first order ODE

and I missed the negative, which really simplifies everything now that I can see that

Re: Nonlinear nonexact first order ODE

Quote:

Originally Posted by

**JJacquelin** Hi Shanter !

Your differential equation is solvable, but very arduously (too difficult to an home work).

I suspect that there is a "-" missing in the wording :

If the equation was : dy/dx = - (3x^2 * y + y^2) / (2x^3 + 3xy) then the integrating factor would be easy to find and the result : (x^3)(y^2)+(y^3)x = C

Hi folks,

How did you solve the modified version with (-) sign included?

Your solution: (x^3)(y^2)+(y^3)x = C

results in :

y'=-(3 x^2 y^2 + y^3)/(2 x^3 y + 3 x y^2)

Re: Nonlinear nonexact first order ODE

Quote:

Originally Posted by

**MaxJasper** How did you solve the modified version with (-) sign included?

Your solution: (x^3)(y^2)+(y^3)x = C

results in :

y'=-(3 x^2 y^2 + y^3)/(2 x^3 y + 3 x y^2)

Hi MaxJasper !

Yes, the solution: (x^3)(y^2)+(y^3)x = C results in :

y' = -(3 x^2 y^2 + y^3)/(2 x^3 y + 3 x y^2) = -(3x^2 * y + y^2) / (2x^3 + 3xy)

Solving the modified version with (-) is rather easy. I let Shanter answer to your question since he found how to do it.

Re: Nonlinear nonexact first order ODE

Differentiate your solution and see that it is different from original diff eq.

Re: Nonlinear nonexact first order ODE

Quote:

Originally Posted by

**MaxJasper** Differentiate your solution and see that it is different from original diff eq.

I don't agree, the solution is allright.

Publish on tbe forum what you did and we will locate your mistake.

Re: Nonlinear nonexact first order ODE

Your solution: (x^3)(y^2)+(y^3)x = C

results in :

y'=-(3 x^2 y^2 + y^3)/(2 x^3 y + 3 x y^2)

that is different from original diff eq. Take a careful look.

Re: Nonlinear nonexact first order ODE

Why don't symplify ?

(y) is a factor of the numerator and of the denominator.

After simplification, compare to the diff. equation (the modified version with - , of course).

Re: Nonlinear nonexact first order ODE

Hi MaxJasper !

do yo agree now ?

Re: Nonlinear nonexact first order ODE

Hey this might be a little late but if you write it out as

Mdx + Ndy = 0

To find the integrating factor I think I used

(Nx - My)/M = A, int factor = e^integral A = y

Note, A must be a function of y only.

I don't have my work with me and I am typing this on my phone but I think this is all right. The rest is straight forward using everything you have.