Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
aditya.sinha
Group Title
if the below diff eq for f not equal to 0 is a family of circles then
 2 years ago
 2 years ago
aditya.sinha Group Title
if the below diff eq for f not equal to 0 is a family of circles then
 2 years ago
 2 years ago

This Question is Closed

aditya.sinha Group TitleBest ResponseYou've already chosen the best response.0
\[d ^{2}y/dx ^{2} =g/f+c\]
 2 years ago

aditya.sinha Group TitleBest ResponseYou've already chosen the best response.0
options :::: a) g,f hv sme sign b>g,f hv opposite sign c>mod g < mod f d> mod g =mod f
 2 years ago

alexray19 Group TitleBest ResponseYou've already chosen the best response.0
I don't know what the question is
 2 years ago

aditya.sinha Group TitleBest ResponseYou've already chosen the best response.0
for the given ques nd a diff eq...select nd calculate the correct option
 2 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.1
Well, the way to evaluate this equation in general is to integrate y'' = g/f + c y' = (g/f)x + cx + c1 y = (g/f + c)x^2 + c1x + c2 This then is the equation of a parabola. So I don't see how to recover a circle from the ODE. In fact, let me say outright this is not the ODE that results from a circle.
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.0
hmm what if g/f + c = 1, then it must result into a circle right?
 2 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.1
To see that, let's start with a circle (xf)^2 + (yg)^2 = c^2 Then differentiating once 2(xf) + 2(yg)y' = 0  (*) and now again 2x + 2y'^2 + 2(yg)y'' = 0 You can manipulate this now to obtain an equation only in y'' by substituting (*) into the second equation. Do that, and you won't recover the original ODE.
 2 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.1
if g/f + c = 1 then y'' = 1 => y' = x + c1 => y = x^2/2 + c1x + c2 which is not a circle for any c1 and c2, but a parabola.
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.0
if g/f + c = 2 then it must circle for sure y" = 2 y' = 2x + c1 y = x^2 + c1x + c2 :D I don't know, must be mathematics
 2 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.1
No, that is NOT the equation of a circle. It is the equation of a parabola.
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.0
oh sorry please ignore me
 2 years ago

JamesJ Group TitleBest ResponseYou've already chosen the best response.1
In other words, I think there's something wrong with the question. Follow the procedure I outlined above to find the expression for y'' from a circle, and perhaps you can figure out what the question should have been.
 2 years ago
See more questions >>>
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.