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,
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.