2.1517   ODE No. 1517

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

$$x^3{y}^{(3)}(x)-2x^3+x^2{y}^{″}(x)+2x{y}^{\prime }(x)-y(x)+\log (x)=0$$ ✓ Mathematica : cpu = 0.288283 (sec), leaf count = 30686 $$\text{Too large to display}$$ ✓ Maple : cpu = 0.454 (sec), leaf count = 866

$$\{y\left(x\right)=c_1{x}^{\frac{(-11+3\sqrt{69}){(44+12\sqrt{69})}^{\frac{2}{3}}}{600}-\frac{{(44+12\sqrt{69})}^{\frac{1}{3}}}{6}+\frac{2}{3}}-x^{\frac{(-11+3\sqrt{69}){(44+12\sqrt{69})}^{\frac{2}{3}}}{600}-\frac{{(44+12\sqrt{69})}^{\frac{1}{3}}}{6}+\frac{2}{3}}(\int -\frac{(2x^3-\ln \left(x\right))(3\sqrt{69}{(44+12\sqrt{69})}^{\frac{1}{3}}-11{(44+12\sqrt{69})}^{\frac{1}{3}}+100){(44+12\sqrt{69})}^{\frac{1}{3}}({\cos }^2\left(\frac{\sqrt{3}{(44+12\sqrt{69})}^{\frac{1}{3}}(3\sqrt{69}{(44+12\sqrt{69})}^{\frac{1}{3}}-11{(44+12\sqrt{69})}^{\frac{1}{3}}+100)\ln \left(x\right)}{1200}\right)+{\sin }^2\left(\frac{\sqrt{3}{(44+12\sqrt{69})}^{\frac{1}{3}}(3\sqrt{69}{(44+12\sqrt{69})}^{\frac{1}{3}}-11{(44+12\sqrt{69})}^{\frac{1}{3}}+100)\ln \left(x\right)}{1200}\right))\sqrt{3}\sqrt{23}{x}^{\frac{(11-3\sqrt{69}){(44+12\sqrt{69})}^{\frac{2}{3}}}{600}+\frac{{(44+12\sqrt{69})}^{\frac{1}{3}}}{6}+\frac{4}{3}}}{13800x^3}dx)+(c_2+\int -\frac{(x^3-\frac{\ln \left(x\right)}{2})(\sqrt{3}(\frac{100}{3}+(\sqrt{69}-\frac{11}{3}){(44+12\sqrt{69})}^{\frac{1}{3}})\cos \left(\frac{\sqrt{3}{(44+12\sqrt{69})}^{\frac{1}{3}}(3\sqrt{69}{(44+12\sqrt{69})}^{\frac{1}{3}}-11{(44+12\sqrt{69})}^{\frac{1}{3}}+100)\ln \left(x\right)}{1200}\right)-3(-\frac{100}{3}+(\sqrt{69}-\frac{11}{3}){(44+12\sqrt{69})}^{\frac{1}{3}})\sin \left(\frac{\sqrt{3}{(44+12\sqrt{69})}^{\frac{1}{3}}(3\sqrt{69}{(44+12\sqrt{69})}^{\frac{1}{3}}-11{(44+12\sqrt{69})}^{\frac{1}{3}}+100)\ln \left(x\right)}{1200}\right)){(44+12\sqrt{69})}^{\frac{1}{3}}\sqrt{23}{x}^{\frac{(-11+3\sqrt{69}){(44+12\sqrt{69})}^{\frac{2}{3}}}{600}-\frac{{(44+12\sqrt{69})}^{\frac{1}{3}}}{6}+\frac{2}{3}}{x}^{\frac{(11-3\sqrt{69}){(44+12\sqrt{69})}^{\frac{2}{3}}}{1200}+\frac{{(44+12\sqrt{69})}^{\frac{1}{3}}}{12}+\frac{2}{3}}}{2300x^3}dx)x^{\frac{(11-3\sqrt{69}){(44+12\sqrt{69})}^{\frac{2}{3}}}{1200}+\frac{{(44+12\sqrt{69})}^{\frac{1}{3}}}{12}+\frac{2}{3}}\cos \left(\frac{\sqrt{3}{(44+12\sqrt{69})}^{\frac{1}{3}}(3\sqrt{69}{(44+12\sqrt{69})}^{\frac{1}{3}}-11{(44+12\sqrt{69})}^{\frac{1}{3}}+100)\ln \left(x\right)}{1200}\right)+(c_3+\int -\frac{3(x^3-\frac{\ln \left(x\right)}{2})((-\frac{100}{3}+(\sqrt{69}-\frac{11}{3}){(44+12\sqrt{69})}^{\frac{1}{3}})\cos \left(\frac{\sqrt{3}{(44+12\sqrt{69})}^{\frac{1}{3}}(3\sqrt{69}{(44+12\sqrt{69})}^{\frac{1}{3}}-11{(44+12\sqrt{69})}^{\frac{1}{3}}+100)\ln \left(x\right)}{1200}\right)+\frac{\sqrt{3}(\frac{100}{3}+(\sqrt{69}-\frac{11}{3}){(44+12\sqrt{69})}^{\frac{1}{3}})\sin \left(\frac{\sqrt{3}{(44+12\sqrt{69})}^{\frac{1}{3}}(3\sqrt{69}{(44+12\sqrt{69})}^{\frac{1}{3}}-11{(44+12\sqrt{69})}^{\frac{1}{3}}+100)\ln \left(x\right)}{1200}\right)}{3}){(44+12\sqrt{69})}^{\frac{1}{3}}\sqrt{23}{x}^{\frac{(-11+3\sqrt{69}){(44+12\sqrt{69})}^{\frac{2}{3}}}{600}-\frac{{(44+12\sqrt{69})}^{\frac{1}{3}}}{6}+\frac{2}{3}}{x}^{\frac{(11-3\sqrt{69}){(44+12\sqrt{69})}^{\frac{2}{3}}}{1200}+\frac{{(44+12\sqrt{69})}^{\frac{1}{3}}}{12}+\frac{2}{3}}}{2300x^3}dx)x^{\frac{(11-3\sqrt{69}){(44+12\sqrt{69})}^{\frac{2}{3}}}{1200}+\frac{{(44+12\sqrt{69})}^{\frac{1}{3}}}{12}+\frac{2}{3}}\sin \left(\frac{\sqrt{3}{(44+12\sqrt{69})}^{\frac{1}{3}}(3\sqrt{69}{(44+12\sqrt{69})}^{\frac{1}{3}}-11{(44+12\sqrt{69})}^{\frac{1}{3}}+100)\ln \left(x\right)}{1200}\right)\}$$