Differential equation problem

Question

anonymous · Answer

I have no idea where to begin on this one to be honest.

anonymous · Answer

@eliassaab sir i've no idea about the question can you please look in to the problem.

anonymous · Answer

This question is from an exam that I did a month ago. Never seen a question like this previously, it caught me completely off guard.

anonymous · Answer

$$
\frac{d \left(x^3-\sin
   (x)\right)}{dx}-4
   \left(x^3-\sin (x)\right)=\-4
   \left(x^3-\sin (x)\right)+3
   x^2-\cos (x)=-4 x^3+3 x^2+4 \sin
   (x)-\cos (x)
$$

anonymous · Answer

Perhaps, it might better sense, if you see the question in its entire form

anonymous · Answer

Apologies for not replying sooner, I was doing another question, thank you @eliassaab  I'll see if I can work out the rest of the other parts of the question now