ODE No. 228

\[ (4 y(x)+11 x-11) y'(x)-25 y(x)-8 x+62=0 \] ✓ Mathematica : cpu = 0.260718 (sec), leaf count = 3357

DSolve[62 - 8*x - 25*y[x] + (-11 + 11*x + 4*y[x])*Derivative[1][y][x] == 0,y[x],x]
 

\[\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 = 0.387 (sec), leaf count = 271

dsolve((4*y(x)+11*x-11)*diff(y(x),x)-25*y(x)-8*x+62 = 0,y(x))
 

\[y \left (x \right ) = \frac {\left (-76 x +28\right ) \left (64-8748 \left (9 x -1\right )^{2} c_{1}+108 \sqrt {43046721}\, \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1}\right ) \left (x -\frac {1}{9}\right )^{2} c_{1}}\right )^{\frac {1}{3}}+4 \left (\left (i \left (64-8748 \left (9 x -1\right )^{2} c_{1}+108 \sqrt {43046721}\, \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1}\right ) \left (x -\frac {1}{9}\right )^{2} c_{1}}\right )^{\frac {2}{3}}-16 i\right ) \sqrt {3}-\left (64-8748 \left (9 x -1\right )^{2} c_{1}+108 \sqrt {43046721}\, \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1}\right ) \left (x -\frac {1}{9}\right )^{2} c_{1}}\right )^{\frac {2}{3}}-16\right ) \left (x +\frac {1}{2}\right )}{8 \left (64-8748 \left (9 x -1\right )^{2} c_{1}+108 \sqrt {43046721}\, \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1}\right ) \left (x -\frac {1}{9}\right )^{2} c_{1}}\right )^{\frac {1}{3}}+\left (i \left (64-8748 \left (9 x -1\right )^{2} c_{1}+108 \sqrt {43046721}\, \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1}\right ) \left (x -\frac {1}{9}\right )^{2} c_{1}}\right )^{\frac {2}{3}}-16 i\right ) \sqrt {3}-\left (64-8748 \left (9 x -1\right )^{2} c_{1}+108 \sqrt {43046721}\, \sqrt {\left (-\frac {32}{177147}+\left (x -\frac {1}{9}\right )^{2} c_{1}\right ) \left (x -\frac {1}{9}\right )^{2} c_{1}}\right )^{\frac {2}{3}}-16}\]