A community for students.
Here's the question you clicked on:
 0 viewing

This Question is Open

matricked
 2 years ago
Best ResponseYou've already chosen the best response.0yup this 1st Order DifEQ

matricked
 2 years ago
Best ResponseYou've already chosen the best response.0you can use y=vx (for homogeneous equations) to solve it

c1c9m9h1
 2 years ago
Best ResponseYou've already chosen the best response.0I don't understand how you determine if its homogeneous, separable...but I understand if its an exact equation...

c1c9m9h1
 2 years ago
Best ResponseYou've already chosen the best response.0I 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..

matricked
 2 years ago
Best ResponseYou've already chosen the best response.0see the sum of the powers of x and y is uniform (here its 2 ) throughout hence homogeneous

c1c9m9h1
 2 years ago
Best ResponseYou've already chosen the best response.0Great! I'm Learning Something Finally!

matricked
 2 years ago
Best ResponseYou've already chosen the best response.0after using y=vx and dy =xdv +vdx the resultant will become a seperable one

c1c9m9h1
 2 years ago
Best ResponseYou've already chosen the best response.0Is 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
 2 years ago
Best ResponseYou've already chosen the best response.0You cannot solve this using separation of variables.

c1c9m9h1
 2 years ago
Best ResponseYou've already chosen the best response.0Yes your right, I understand that its not an exact equation..

c1c9m9h1
 2 years ago
Best ResponseYou've already chosen the best response.0I have 6 problems that are due in 45 mins... I need help!!!

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.2Let'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
 2 years ago
Best ResponseYou've already chosen the best response.2This 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
 2 years ago
Best ResponseYou've already chosen the best response.2***I dropped a half in front of the (y/x)^2 term, so v + xv' = (1/2) ( 2 + v + v^2 )

c1c9m9h1
 2 years ago
Best ResponseYou've already chosen the best response.0I keep getting different answers though when i do that... i have the solutions just can get there while showing my work

c1c9m9h1
 2 years ago
Best ResponseYou've already chosen the best response.0Anyone who can help solve these problems will be a life saver!

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.2Well, 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.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.