anonymous
  • anonymous
(2x^2+xy+y^2)dx + 2x^2 dy=0 How Do I Solve This 1st Order DifEQ? Help Please!!
Differential Equations
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
yup this 1st Order DifEQ
anonymous
  • anonymous
you can use y=vx (for homogeneous equations) to solve it
anonymous
  • anonymous
I don't understand how you determine if its homogeneous, separable...but I understand if its an exact equation...

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
then dy =xdv +vdx
anonymous
  • anonymous
I have 6 problems that i have to do and i have the answers but i just dont understand how to do the work to get the answer unless its an exact equation..
anonymous
  • anonymous
see the sum of the powers of x and y is uniform (here its 2 ) throughout hence homogeneous
anonymous
  • anonymous
Great! I'm Learning Something Finally!
anonymous
  • anonymous
welcome
anonymous
  • anonymous
after using y=vx and dy =xdv +vdx the resultant will become a seperable one
anonymous
  • anonymous
Is there a certain formula that is out there where i can solve these problems if they are separable or homogenous or any other thing out there?? I really want to learn this stuff
abb0t
  • abb0t
You cannot solve this using separation of variables.
anonymous
  • anonymous
Yes your right, I understand that its not an exact equation..
anonymous
  • anonymous
I have 6 problems that are due in 45 mins... I need help!!!
JamesJ
  • JamesJ
Let's start from the beginning (2x^2+xy+y^2)dx + 2x^2 dy=0 implies that dy/dx = -(2x^2+xy+y^2)/(2x^2) and hence dy/dx = -1 - (1/2)(y/x) - (y/x)^2
JamesJ
  • JamesJ
This is what is called a homogeneous equation. It is one of the meanings of the word homogeneous for differential equations. The substitution 'trick' for such equations is to write v = y/x and hence y = vx which implies y' = v + xv' Therefore we can rewrite the equation above as v + xv' = - (1 + (1/2)v + v^2) This now IS a separable equation which you can solve using standard techniques to find the function v(x). Once you have done that, substitute back v(x) = y(x)/x to solve for y(x)
JamesJ
  • JamesJ
***I dropped a half in front of the (y/x)^2 term, so v + xv' = -(1/2) ( 2 + v + v^2 )
JamesJ
  • JamesJ
Make sense?
anonymous
  • anonymous
I keep getting different answers though when i do that... i have the solutions just can get there while showing my work
anonymous
  • anonymous
Anyone who can help solve these problems will be a life saver!
JamesJ
  • JamesJ
Well, v + xv' = -(1/2) ( 2 + v + v^2 ) implies -2x v' = v^2 + 3v + 2 = (v+2)(v+1) hence separating \[ -2\int \left( \frac{A}{v+2} + \frac{B}{v+1} \right) dv = \int \frac{dx}{x} \] You take it from there.

Looking for something else?

Not the answer you are looking for? Search for more explanations.