Question 1160312
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I will do it, but I will use more compact designation  " y' "  for the derivative {{{(dy)/(dx)}}}.



    24x^5 + (12x^3y + 3x^4*y') - 4y^6 -24xy^5*y' = 0


Now re-group the terms, collecting the terms with  " y' " in one group


    24x^5 + 12x^3y - 4y^6 = (-3x^4 + 24y^5)*y'


Now express  y'


    y' = {{{(24x^5 + 12x^3y - 4y^6)/(-3x^4 + 24y^5)}}}.


It is your answer.
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Solved.