Udo thank you very much for helping me in this stage of confusion, but I am still confused, my question is, should I enter in Mathematica the differential equation in question as you have suggested above, or do I have to do anything different, because if I do the following steps i get a very long and also very complicated
ode = (5 x + 4 y[x]) + (4 x - 8 y[x]^3) y'[x] == 0;
DSolve[ode, y[x], x]
with respect to the error of such as cite the equation, i realized after having published my doubt in the community but thanks for reminding me, Is there any way to obtain some more compact solution?, although it is like the one that my teacher gave
Thanks in advance
Luis Ledesma