3.228   ODE No. 228

$$\boxed{{\displaystyle (4y\left(x\right)+11x-11)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-25y\left(x\right)-8x+62=0}}$$

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

Mathematica: cpu = 0.196025 (sec), leaf count = 3357 $$\{\{y(x)\to \frac{1}{4(-\frac{\sqrt[3]{2}(59049\cosh \left(\frac{3c_1}{8}\right)x^2+59049\sinh \left(\frac{3c_1}{8}\right)x^2-13122\cosh \left(\frac{3c_1}{8}\right)x-13122\sinh \left(\frac{3c_1}{8}\right)x+729\cosh \left(\frac{3c_1}{8}\right)+729\sinh \left(\frac{3c_1}{8}\right)-729)}{81(9x-1)(81\cosh \left(\frac{3c_1}{8}\right)x^2+81\sinh \left(\frac{3c_1}{8}\right)x^2-18\cosh \left(\frac{3c_1}{8}\right)x-18\sinh \left(\frac{3c_1}{8}\right)x+\cosh \left(\frac{3c_1}{8}\right)+\sinh \left(\frac{3c_1}{8}\right)-1)\sqrt[3]{-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)+\sqrt{4(59049\cosh \left(\frac{3c_1}{8}\right)x^2+59049\sinh \left(\frac{3c_1}{8}\right)x^2-13122\cosh \left(\frac{3c_1}{8}\right)x-13122\sinh \left(\frac{3c_1}{8}\right)x+729\cosh \left(\frac{3c_1}{8}\right)+729\sinh \left(\frac{3c_1}{8}\right)-729){}^3+(-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)-39366){}^2}-39366}}+\frac{\sqrt[3]{-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)+\sqrt{4(59049\cosh \left(\frac{3c_1}{8}\right)x^2+59049\sinh \left(\frac{3c_1}{8}\right)x^2-13122\cosh \left(\frac{3c_1}{8}\right)x-13122\sinh \left(\frac{3c_1}{8}\right)x+729\cosh \left(\frac{3c_1}{8}\right)+729\sinh \left(\frac{3c_1}{8}\right)-729){}^3+(-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)-39366){}^2}-39366}}{81\sqrt[3]{2}(9x-1)(81\cosh \left(\frac{3c_1}{8}\right)x^2+81\sinh \left(\frac{3c_1}{8}\right)x^2-18\cosh \left(\frac{3c_1}{8}\right)x-18\sinh \left(\frac{3c_1}{8}\right)x+\cosh \left(\frac{3c_1}{8}\right)+\sinh \left(\frac{3c_1}{8}\right)-1)}+\frac{1}{3(9x-1)})}-\frac{11(x-1)}{4}\},\{y(x)\to \frac{1}{4(\frac{(1+i\sqrt{3})(59049\cosh \left(\frac{3c_1}{8}\right)x^2+59049\sinh \left(\frac{3c_1}{8}\right)x^2-13122\cosh \left(\frac{3c_1}{8}\right)x-13122\sinh \left(\frac{3c_1}{8}\right)x+729\cosh \left(\frac{3c_1}{8}\right)+729\sinh \left(\frac{3c_1}{8}\right)-729)}{812^{2/3}(9x-1)(81\cosh \left(\frac{3c_1}{8}\right)x^2+81\sinh \left(\frac{3c_1}{8}\right)x^2-18\cosh \left(\frac{3c_1}{8}\right)x-18\sinh \left(\frac{3c_1}{8}\right)x+\cosh \left(\frac{3c_1}{8}\right)+\sinh \left(\frac{3c_1}{8}\right)-1)\sqrt[3]{-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)+\sqrt{4(59049\cosh \left(\frac{3c_1}{8}\right)x^2+59049\sinh \left(\frac{3c_1}{8}\right)x^2-13122\cosh \left(\frac{3c_1}{8}\right)x-13122\sinh \left(\frac{3c_1}{8}\right)x+729\cosh \left(\frac{3c_1}{8}\right)+729\sinh \left(\frac{3c_1}{8}\right)-729){}^3+(-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)-39366){}^2}-39366}}-\frac{(1-i\sqrt{3})\sqrt[3]{-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)+\sqrt{4(59049\cosh \left(\frac{3c_1}{8}\right)x^2+59049\sinh \left(\frac{3c_1}{8}\right)x^2-13122\cosh \left(\frac{3c_1}{8}\right)x-13122\sinh \left(\frac{3c_1}{8}\right)x+729\cosh \left(\frac{3c_1}{8}\right)+729\sinh \left(\frac{3c_1}{8}\right)-729){}^3+(-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)-39366){}^2}-39366}}{162\sqrt[3]{2}(9x-1)(81\cosh \left(\frac{3c_1}{8}\right)x^2+81\sinh \left(\frac{3c_1}{8}\right)x^2-18\cosh \left(\frac{3c_1}{8}\right)x-18\sinh \left(\frac{3c_1}{8}\right)x+\cosh \left(\frac{3c_1}{8}\right)+\sinh \left(\frac{3c_1}{8}\right)-1)}+\frac{1}{3(9x-1)})}-\frac{11(x-1)}{4}\},\{y(x)\to \frac{1}{4(\frac{(1-i\sqrt{3})(59049\cosh \left(\frac{3c_1}{8}\right)x^2+59049\sinh \left(\frac{3c_1}{8}\right)x^2-13122\cosh \left(\frac{3c_1}{8}\right)x-13122\sinh \left(\frac{3c_1}{8}\right)x+729\cosh \left(\frac{3c_1}{8}\right)+729\sinh \left(\frac{3c_1}{8}\right)-729)}{812^{2/3}(9x-1)(81\cosh \left(\frac{3c_1}{8}\right)x^2+81\sinh \left(\frac{3c_1}{8}\right)x^2-18\cosh \left(\frac{3c_1}{8}\right)x-18\sinh \left(\frac{3c_1}{8}\right)x+\cosh \left(\frac{3c_1}{8}\right)+\sinh \left(\frac{3c_1}{8}\right)-1)\sqrt[3]{-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)+\sqrt{4(59049\cosh \left(\frac{3c_1}{8}\right)x^2+59049\sinh \left(\frac{3c_1}{8}\right)x^2-13122\cosh \left(\frac{3c_1}{8}\right)x-13122\sinh \left(\frac{3c_1}{8}\right)x+729\cosh \left(\frac{3c_1}{8}\right)+729\sinh \left(\frac{3c_1}{8}\right)-729){}^3+(-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)-39366){}^2}-39366}}-\frac{(1+i\sqrt{3})\sqrt[3]{-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)+\sqrt{4(59049\cosh \left(\frac{3c_1}{8}\right)x^2+59049\sinh \left(\frac{3c_1}{8}\right)x^2-13122\cosh \left(\frac{3c_1}{8}\right)x-13122\sinh \left(\frac{3c_1}{8}\right)x+729\cosh \left(\frac{3c_1}{8}\right)+729\sinh \left(\frac{3c_1}{8}\right)-729){}^3+(-258280326\cosh \left(\frac{3c_1}{4}\right)x^4-258280326\sinh \left(\frac{3c_1}{4}\right)x^4+114791256\cosh \left(\frac{3c_1}{4}\right)x^3+114791256\sinh \left(\frac{3c_1}{4}\right)x^3+6377292\cosh \left(\frac{3c_1}{8}\right)x^2-19131876\cosh \left(\frac{3c_1}{4}\right)x^2+6377292\sinh \left(\frac{3c_1}{8}\right)x^2-19131876\sinh \left(\frac{3c_1}{4}\right)x^2-1417176\cosh \left(\frac{3c_1}{8}\right)x+1417176\cosh \left(\frac{3c_1}{4}\right)x-1417176\sinh \left(\frac{3c_1}{8}\right)x+1417176\sinh \left(\frac{3c_1}{4}\right)x+78732\cosh \left(\frac{3c_1}{8}\right)-39366\cosh \left(\frac{3c_1}{4}\right)+78732\sinh \left(\frac{3c_1}{8}\right)-39366\sinh \left(\frac{3c_1}{4}\right)-39366){}^2}-39366}}{162\sqrt[3]{2}(9x-1)(81\cosh \left(\frac{3c_1}{8}\right)x^2+81\sinh \left(\frac{3c_1}{8}\right)x^2-18\cosh \left(\frac{3c_1}{8}\right)x-18\sinh \left(\frac{3c_1}{8}\right)x+\cosh \left(\frac{3c_1}{8}\right)+\sinh \left(\frac{3c_1}{8}\right)-1)}+\frac{1}{3(9x-1)})}-\frac{11(x-1)}{4}\}\}$$

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