Find the differential equation of the family of curves y=c(x-c)^2 where c is a parameter.

I don't know the solution to this problem. Shall i get help to get the solution to this problem?

Okay,

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- Nov 20th 2011, 03:54 AMVinodDifferential equation of the family of curves y=c(x-c)^2

Find the differential equation of the family of curves y=c(x-c)^2 where c is a parameter.

I don't know the solution to this problem. Shall i get help to get the solution to this problem?

Okay, - Nov 20th 2011, 04:42 AMJesterRe: Differential equation of the family of curves y=c(x-c)^2
Take the $\displaystyle \ln $ of both sides

$\displaystyle \ln y = \ln c + 2\ln (x-c)$

Then differentiate

$\displaystyle \frac{y'}{y} = \frac{2}{x-c}$

solve for c and sub back into original ODE.

You know, there are many ODEs that has this as a solution. - Nov 21st 2011, 05:49 AMVinodRe: Differential equation of the family of curves y=c(x-c)^2