3.228   ODE No. 228

\[ \boxed { \left ( 4\,y \left ( x \right ) +11\,x-11 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -25\,y \left ( x \right ) -8\,x+62=0} \]

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

Mathematica: cpu = 0.196025 (sec), leaf count = 3357 \[ \left \{\left \{y(x)\to \frac {1}{4 \left (-\frac {\sqrt [3]{2} \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right )}{81 (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right ) \sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}+\frac {\sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}{81 \sqrt [3]{2} (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right )}+\frac {1}{3 (9 x-1)}\right )}-\frac {11 (x-1)}{4}\right \},\left \{y(x)\to \frac {1}{4 \left (\frac {\left (1+i \sqrt {3}\right ) \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right )}{81\ 2^{2/3} (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right ) \sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}{162 \sqrt [3]{2} (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right )}+\frac {1}{3 (9 x-1)}\right )}-\frac {11 (x-1)}{4}\right \},\left \{y(x)\to \frac {1}{4 \left (\frac {\left (1-i \sqrt {3}\right ) \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right )}{81\ 2^{2/3} (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right ) \sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )+\sqrt {4 \left (59049 \cosh \left (\frac {3 c_1}{8}\right ) x^2+59049 \sinh \left (\frac {3 c_1}{8}\right ) x^2-13122 \cosh \left (\frac {3 c_1}{8}\right ) x-13122 \sinh \left (\frac {3 c_1}{8}\right ) x+729 \cosh \left (\frac {3 c_1}{8}\right )+729 \sinh \left (\frac {3 c_1}{8}\right )-729\right ){}^3+\left (-258280326 \cosh \left (\frac {3 c_1}{4}\right ) x^4-258280326 \sinh \left (\frac {3 c_1}{4}\right ) x^4+114791256 \cosh \left (\frac {3 c_1}{4}\right ) x^3+114791256 \sinh \left (\frac {3 c_1}{4}\right ) x^3+6377292 \cosh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \cosh \left (\frac {3 c_1}{4}\right ) x^2+6377292 \sinh \left (\frac {3 c_1}{8}\right ) x^2-19131876 \sinh \left (\frac {3 c_1}{4}\right ) x^2-1417176 \cosh \left (\frac {3 c_1}{8}\right ) x+1417176 \cosh \left (\frac {3 c_1}{4}\right ) x-1417176 \sinh \left (\frac {3 c_1}{8}\right ) x+1417176 \sinh \left (\frac {3 c_1}{4}\right ) x+78732 \cosh \left (\frac {3 c_1}{8}\right )-39366 \cosh \left (\frac {3 c_1}{4}\right )+78732 \sinh \left (\frac {3 c_1}{8}\right )-39366 \sinh \left (\frac {3 c_1}{4}\right )-39366\right ){}^2}-39366}}{162 \sqrt [3]{2} (9 x-1) \left (81 \cosh \left (\frac {3 c_1}{8}\right ) x^2+81 \sinh \left (\frac {3 c_1}{8}\right ) x^2-18 \cosh \left (\frac {3 c_1}{8}\right ) x-18 \sinh \left (\frac {3 c_1}{8}\right ) x+\cosh \left (\frac {3 c_1}{8}\right )+\sinh \left (\frac {3 c_1}{8}\right )-1\right )}+\frac {1}{3 (9 x-1)}\right )}-\frac {11 (x-1)}{4}\right \}\right \} \]

Maple: cpu = 0.280 (sec), leaf count = 377 \[ \left \{ y \left ( x \right ) ={\frac {22}{9}}+36\,{(9\,x-1) \left ( -1/ 27\,\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\, \sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9 \,x-1 \right ) ^{2}{\it \_C1}}}-{\frac {16}{27\,\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1 }}}}}-{\frac {19}{27}}+2\,i\sqrt {3} \left ( {\frac {\sqrt [3]{64-8748 \, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x -1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}}{54}}-{\frac {8}{27\,\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{ {\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}}} \right ) \right ) \left ( -3\,\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{ \it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2 }-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}-48\,{\frac {1}{\sqrt [3] {64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}}}+24+162\,i\sqrt {3} \left ( {\frac {\sqrt [3 ]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}}}}{54}}-{\frac {8}{27\,\sqrt [3]{64-8748\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1}+108\,\sqrt {6561\, \left ( 9\,x-1 \right ) ^{4}{{\it \_C1}}^{2}-96\, \left ( 9\,x-1 \right ) ^{2}{\it \_C1 }}}}} \right ) \right ) ^{-1}} \right \} \]