Thread: Find a differential equation given solution

Find a di®erential equation whose solution is the two parameter fam-

ily of curves ln y = c1*x^2+ c2.

I've gotten this far:
y= e^(c1*x^2+ c2)

y'= 2*c1*x* (e^(c1*x^2+ c2).

I also found y''. But for the world of it I cannot figure out the differential equation from y, y' and y''.

Really appreciate your help!

or if you prefer