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if the below diff eq for f not equal to 0 is a family of circles then
 2 years ago
 2 years ago
if the below diff eq for f not equal to 0 is a family of circles then
 2 years ago
 2 years ago

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

aditya.sinhaBest 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

alexray19Best ResponseYou've already chosen the best response.0
I don't know what the question is
 2 years ago

aditya.sinhaBest 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

JamesJBest 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

Ishaan94Best 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

JamesJBest 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

JamesJBest 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

Ishaan94Best 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

JamesJBest 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

Ishaan94Best ResponseYou've already chosen the best response.0
oh sorry please ignore me
 2 years ago

JamesJBest 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
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