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

**Vinod** · November 20th 2011, 03:54 AM

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,

**Danny** · November 20th 2011, 04:42 AM

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.

**Vinod** · November 21st 2011, 05:49 AM

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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