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

1. ## 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,

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

Take the $\ln$ of both sides

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

Then differentiate

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

solve for c and sub back into original ODE.

You know, there are many ODEs that has this as a solution.

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

Originally Posted by Danny
Take the $\ln$ of both sides

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

Then differentiate

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

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.

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# order of differential equation whose soln is y=c(x-c)2

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