Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

Starting with the equation


I could only get the general solution using DSolve:

DSolve[{y''[x] x^2 == y'[x]^2}, y[x], x]
(* {{y[x] -> -(x/C[1]) + C[2] - Log[1 - x C[1]]/C[1]^2}} *)

However, I failed to get the singular solutions y[x] -> x^2/2 + C[1] and y[x] -> C[1]. So, how can I get them?

share|improve this question

1 Answer 1

up vote 7 down vote accepted

With :

sol = DSolve[{x^2 y''[x] == y'[x]^2}, y[x], x][[1, 1, 2]];

Limit[sol, C[1] -> 0]
(* x^2/2 + C[2] *)

Limit[sol, C[1] -> Infinity]
(* C[2] *)
share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.