3.948   ODE No. 948

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-216\,{\frac {y \left ( x \right ) }{-216\, \left ( y \left ( x \right ) \right ) ^{4}-252\, \left ( y \left ( x \right ) \right ) ^{3}-396\, \left ( y \left ( x \right ) \right ) ^{2}-216\,y \left ( x \right ) +36\,{x}^{2}-72\,xy \left ( x \right ) +60\, \left ( y \left ( x \right ) \right ) ^{5}-36\,x \left ( y \left ( x \right ) \right ) ^{3}-72\,x \left ( y \left ( x \right ) \right ) ^{2}-24\,x \left ( y \left ( x \right ) \right ) ^{4}+4\, \left ( y \left ( x \right ) \right ) ^{8}+12\, \left ( y \left ( x \right ) \right ) ^{7}+33\, \left ( y \left ( x \right ) \right ) ^{6}}}=0} \]

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

Mathematica: cpu = 0.259033 (sec), leaf count = 39 \[ \text {Solve}\left [\frac {36}{y(x) \left (2 y(x)^3+3 y(x)^2+6 y(x)+6\right )-6 x}+\log (y(x))=c_1,y(x)\right ] \]

Maple: cpu = 0.140 (sec), leaf count = 68 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( -12\,{\it \_C1}\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{4}-2\, \left ( {{\rm e}^ {{\it \_Z}}} \right ) ^{4}{\it \_Z}-18\,{\it \_C1}\, \left ( {{\rm e}^{{ \it \_Z}}} \right ) ^{3}-3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{3}{ \it \_Z}-36\,{\it \_C1}\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-6 \,{\it \_Z}\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-36\,{\it \_C1} \,{{\rm e}^{{\it \_Z}}}-6\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+36\,x{\it \_C1}+6\,{\it \_Z}\,x-36 \right ) }} \right \} \]