# Differential equation of the family of curves y=c(x-c)^2

• Nov 20th 2011, 03:54 AM
Vinod
Differential 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 AM
Jester
Re: 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 AM
Vinod
Re: Differential equation of the family of curves y=c(x-c)^2
Quote:

Originally Posted by Danny
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.

Danny,
MHF helper,
Hello,
I got the answer to the problem. Thanks.