2.228   ODE No. 228

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

$$(4y(x)+11x-11)y^{\prime }(x)-25y(x)-8x+62=0$$ ✓ Mathematica : cpu = 0.404245 (sec), leaf count = 1677

$$\{\{y(x)\to \frac{1}{4}(\frac{3(9x-1)}{\frac{\sqrt[3]{-6561\cosh \left(\frac{3c_1}{4}\right)x^4-6561\sinh \left(\frac{3c_1}{4}\right)x^4+2916\cosh \left(\frac{3c_1}{4}\right)x^3+2916\sinh \left(\frac{3c_1}{4}\right)x^3+162\cosh \left(\frac{3c_1}{8}\right)x^2-486\cosh \left(\frac{3c_1}{4}\right)x^2+162\sinh \left(\frac{3c_1}{8}\right)x^2-486\sinh \left(\frac{3c_1}{4}\right)x^2-36\cosh \left(\frac{3c_1}{8}\right)x+36\cosh \left(\frac{3c_1}{4}\right)x-36\sinh \left(\frac{3c_1}{8}\right)x+36\sinh \left(\frac{3c_1}{4}\right)x+2\cosh \left(\frac{3c_1}{8}\right)-\cosh \left(\frac{3c_1}{4}\right)+2\sinh \left(\frac{3c_1}{8}\right)-\sinh \left(\frac{3c_1}{4}\right)+\sqrt{(1-9x{)}^2(9x(9x-2)\cosh \left(\frac{3c_1}{16}\right)+(81x^2-18x+2)\sinh \left(\frac{3c_1}{16}\right)){}^3(\cosh \left(\frac{15c_1}{16}\right)+\sinh \left(\frac{15c_1}{16}\right))}-1}}{\cosh \left(\frac{3c_1}{8}\right)(1-9x{)}^2+\sinh \left(\frac{3c_1}{8}\right)(1-9x{)}^2-1}+1-\frac{1}{\sqrt[3]{-6561\cosh \left(\frac{3c_1}{4}\right)x^4-6561\sinh \left(\frac{3c_1}{4}\right)x^4+2916\cosh \left(\frac{3c_1}{4}\right)x^3+2916\sinh \left(\frac{3c_1}{4}\right)x^3+162\cosh \left(\frac{3c_1}{8}\right)x^2-486\cosh \left(\frac{3c_1}{4}\right)x^2+162\sinh \left(\frac{3c_1}{8}\right)x^2-486\sinh \left(\frac{3c_1}{4}\right)x^2-36\cosh \left(\frac{3c_1}{8}\right)x+36\cosh \left(\frac{3c_1}{4}\right)x-36\sinh \left(\frac{3c_1}{8}\right)x+36\sinh \left(\frac{3c_1}{4}\right)x+2\cosh \left(\frac{3c_1}{8}\right)-\cosh \left(\frac{3c_1}{4}\right)+2\sinh \left(\frac{3c_1}{8}\right)-\sinh \left(\frac{3c_1}{4}\right)+\sqrt{(1-9x{)}^2(9x(9x-2)\cosh \left(\frac{3c_1}{16}\right)+(81x^2-18x+2)\sinh \left(\frac{3c_1}{16}\right)){}^3(\cosh \left(\frac{15c_1}{16}\right)+\sinh \left(\frac{15c_1}{16}\right))}-1}}}-11(x-1))\},\{y(x)\to \frac{1}{4}(\frac{6(9x-1)}{\frac{i(i+\sqrt{3})\sqrt[3]{-6561\cosh \left(\frac{3c_1}{4}\right)x^4-6561\sinh \left(\frac{3c_1}{4}\right)x^4+2916\cosh \left(\frac{3c_1}{4}\right)x^3+2916\sinh \left(\frac{3c_1}{4}\right)x^3+162\cosh \left(\frac{3c_1}{8}\right)x^2-486\cosh \left(\frac{3c_1}{4}\right)x^2+162\sinh \left(\frac{3c_1}{8}\right)x^2-486\sinh \left(\frac{3c_1}{4}\right)x^2-36\cosh \left(\frac{3c_1}{8}\right)x+36\cosh \left(\frac{3c_1}{4}\right)x-36\sinh \left(\frac{3c_1}{8}\right)x+36\sinh \left(\frac{3c_1}{4}\right)x+2\cosh \left(\frac{3c_1}{8}\right)-\cosh \left(\frac{3c_1}{4}\right)+2\sinh \left(\frac{3c_1}{8}\right)-\sinh \left(\frac{3c_1}{4}\right)+\sqrt{(1-9x{)}^2(9x(9x-2)\cosh \left(\frac{3c_1}{16}\right)+(81x^2-18x+2)\sinh \left(\frac{3c_1}{16}\right)){}^3(\cosh \left(\frac{15c_1}{16}\right)+\sinh \left(\frac{15c_1}{16}\right))}-1}}{\cosh \left(\frac{3c_1}{8}\right)(1-9x{)}^2+\sinh \left(\frac{3c_1}{8}\right)(1-9x{)}^2-1}+2+\frac{1+i\sqrt{3}}{\sqrt[3]{-6561\cosh \left(\frac{3c_1}{4}\right)x^4-6561\sinh \left(\frac{3c_1}{4}\right)x^4+2916\cosh \left(\frac{3c_1}{4}\right)x^3+2916\sinh \left(\frac{3c_1}{4}\right)x^3+162\cosh \left(\frac{3c_1}{8}\right)x^2-486\cosh \left(\frac{3c_1}{4}\right)x^2+162\sinh \left(\frac{3c_1}{8}\right)x^2-486\sinh \left(\frac{3c_1}{4}\right)x^2-36\cosh \left(\frac{3c_1}{8}\right)x+36\cosh \left(\frac{3c_1}{4}\right)x-36\sinh \left(\frac{3c_1}{8}\right)x+36\sinh \left(\frac{3c_1}{4}\right)x+2\cosh \left(\frac{3c_1}{8}\right)-\cosh \left(\frac{3c_1}{4}\right)+2\sinh \left(\frac{3c_1}{8}\right)-\sinh \left(\frac{3c_1}{4}\right)+\sqrt{(1-9x{)}^2(9x(9x-2)\cosh \left(\frac{3c_1}{16}\right)+(81x^2-18x+2)\sinh \left(\frac{3c_1}{16}\right)){}^3(\cosh \left(\frac{15c_1}{16}\right)+\sinh \left(\frac{15c_1}{16}\right))}-1}}}-11(x-1))\},\{y(x)\to \frac{1}{4}(\frac{6(9x-1)}{-\frac{i(-i+\sqrt{3})\sqrt[3]{-6561\cosh \left(\frac{3c_1}{4}\right)x^4-6561\sinh \left(\frac{3c_1}{4}\right)x^4+2916\cosh \left(\frac{3c_1}{4}\right)x^3+2916\sinh \left(\frac{3c_1}{4}\right)x^3+162\cosh \left(\frac{3c_1}{8}\right)x^2-486\cosh \left(\frac{3c_1}{4}\right)x^2+162\sinh \left(\frac{3c_1}{8}\right)x^2-486\sinh \left(\frac{3c_1}{4}\right)x^2-36\cosh \left(\frac{3c_1}{8}\right)x+36\cosh \left(\frac{3c_1}{4}\right)x-36\sinh \left(\frac{3c_1}{8}\right)x+36\sinh \left(\frac{3c_1}{4}\right)x+2\cosh \left(\frac{3c_1}{8}\right)-\cosh \left(\frac{3c_1}{4}\right)+2\sinh \left(\frac{3c_1}{8}\right)-\sinh \left(\frac{3c_1}{4}\right)+\sqrt{(1-9x{)}^2(9x(9x-2)\cosh \left(\frac{3c_1}{16}\right)+(81x^2-18x+2)\sinh \left(\frac{3c_1}{16}\right)){}^3(\cosh \left(\frac{15c_1}{16}\right)+\sinh \left(\frac{15c_1}{16}\right))}-1}}{\cosh \left(\frac{3c_1}{8}\right)(1-9x{)}^2+\sinh \left(\frac{3c_1}{8}\right)(1-9x{)}^2-1}+2+\frac{1-i\sqrt{3}}{\sqrt[3]{-6561\cosh \left(\frac{3c_1}{4}\right)x^4-6561\sinh \left(\frac{3c_1}{4}\right)x^4+2916\cosh \left(\frac{3c_1}{4}\right)x^3+2916\sinh \left(\frac{3c_1}{4}\right)x^3+162\cosh \left(\frac{3c_1}{8}\right)x^2-486\cosh \left(\frac{3c_1}{4}\right)x^2+162\sinh \left(\frac{3c_1}{8}\right)x^2-486\sinh \left(\frac{3c_1}{4}\right)x^2-36\cosh \left(\frac{3c_1}{8}\right)x+36\cosh \left(\frac{3c_1}{4}\right)x-36\sinh \left(\frac{3c_1}{8}\right)x+36\sinh \left(\frac{3c_1}{4}\right)x+2\cosh \left(\frac{3c_1}{8}\right)-\cosh \left(\frac{3c_1}{4}\right)+2\sinh \left(\frac{3c_1}{8}\right)-\sinh \left(\frac{3c_1}{4}\right)+\sqrt{(1-9x{)}^2(9x(9x-2)\cosh \left(\frac{3c_1}{16}\right)+(81x^2-18x+2)\sinh \left(\frac{3c_1}{16}\right)){}^3(\cosh \left(\frac{15c_1}{16}\right)+\sinh \left(\frac{15c_1}{16}\right))}-1}}}-11(x-1))\}\}$$

✓ Maple : cpu = 0.451 (sec), leaf count = 271

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