Separation of variables (ODEs)

Question

Here is the question I am currently stuck on:

Here is what I have done so far:

My apologies as I understand this post seems fairly lengthy. However I cannot seem to get the final answer with x in terms of t (the solution is x(t)=((t^2) + C)^3 + 1). I am stuck on what to do after the last stage of my working which I have shown in the images.

any help is appreciated, thank you

Answer 1

since c is a constant it can be anything put c=3d where d is a new constant.now we can cancel 3 for all the sides.now cube both the sides and you get a matching answer.Though your answer was also right it seemed wrong due to the constant which can be anything.If you would reverse steps and make a differential equation out of your answer it would also give the question as it is.