Dear Peter,
no need to double post the question to me and to Mariusz. There are some problems with the way you type in your equations. First of all, the parenthesis do not match up. I suppose there is one missing at the end. Also, Mathematica/WoflramAlpha would probably need to know what the independent variable is (it could be "a", i.e. y could be a function of a, for example). Also, if you type ax instead of a x the Wolfram Language will take that to be the name of a variable not the product of "a" and "x".
Even if you fix this, WolframAlpha does not provide a solution. Mathematica and the online products, however, do give you a solution:
DSolve[y'[x] == a (1 - (2 k/c) (y[x] + a x)) (1 - (2/c) (d - (a (x^2)/2))), y[x], x]
gives
I would consider moving over to the WolframCloud for this kind of application.
Best wishes,
Marco
