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 = 0.40462 (sec), leaf count = 30686

$$\text{Too large to display}$$

✓ Maple : cpu = 0.717 (sec), leaf count = 1771

$$\{y\left(x\right)=-\int -\frac{5{\left(x^{1/12\sqrt[3]{44+12\sqrt{69}}+2/3+\frac{11{(44+12\sqrt{69})}^{2/3}}{1200}-\frac{\sqrt{69}{(44+12\sqrt{69})}^{2/3}}{400}}\right)}^2\sqrt[3]{44+12\sqrt{69}}(\ln \left(x\right)-2x^3)}{2x^3(3\sqrt{3}\sqrt{23}+11)(11\sqrt{3}\sqrt{23}-207)}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}{(\sin \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right))}^2+3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}{(\cos \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right))}^2-11\sqrt[3]{44+12\sqrt{69}}{(\sin \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right))}^2-11\sqrt[3]{44+12\sqrt{69}}{(\cos \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right))}^2+100{(\sin \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right))}^2+100{(\cos \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right))}^2)\mathrm{d}x{x}^{\frac{\sqrt{69}{(44+12\sqrt{69})}^{\frac{2}{3}}}{200}-\frac{11{(44+12\sqrt{69})}^{2/3}}{600}-\frac{\sqrt[3]{44+12\sqrt{69}}}{6}+\frac{2}{3}}-\int -\frac{5x^{\frac{\sqrt{69}{(44+12\sqrt{69})}^{2/3}}{200}-\frac{11{(44+12\sqrt{69})}^{2/3}}{600}-1/6\sqrt[3]{44+12\sqrt{69}}+2/3}{x}^{1/12\sqrt[3]{44+12\sqrt{69}}+2/3+\frac{11{(44+12\sqrt{69})}^{2/3}}{1200}-\frac{\sqrt{69}{(44+12\sqrt{69})}^{2/3}}{400}}\sqrt[3]{44+12\sqrt{69}}(\ln \left(x\right)-2x^3)\sqrt{3}}{6x^3(3\sqrt{3}\sqrt{23}+11)(11\sqrt{3}\sqrt{23}-207)}(-3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}\cos \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)\sqrt{3}+9\sqrt[3]{44+12\sqrt{69}}\sqrt{69}\sin \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)+11\sqrt[3]{44+12\sqrt{69}}\sqrt{3}\cos \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)-33\sqrt[3]{44+12\sqrt{69}}\sin \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)-100\cos \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)\sqrt{3}-300\sin \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right))\mathrm{d}x{x}^{\frac{\sqrt[3]{44+12\sqrt{69}}}{12}+\frac{2}{3}+\frac{11{(44+12\sqrt{69})}^{2/3}}{1200}-\frac{\sqrt{69}{(44+12\sqrt{69})}^{\frac{2}{3}}}{400}}\cos \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)+\int -\frac{5x^{\frac{\sqrt{69}{(44+12\sqrt{69})}^{2/3}}{200}-\frac{11{(44+12\sqrt{69})}^{2/3}}{600}-1/6\sqrt[3]{44+12\sqrt{69}}+2/3}{x}^{1/12\sqrt[3]{44+12\sqrt{69}}+2/3+\frac{11{(44+12\sqrt{69})}^{2/3}}{1200}-\frac{\sqrt{69}{(44+12\sqrt{69})}^{2/3}}{400}}\sqrt[3]{44+12\sqrt{69}}(\ln \left(x\right)-2x^3)\sqrt{3}}{6x^3(3\sqrt{3}\sqrt{23}+11)(11\sqrt{3}\sqrt{23}-207)}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}\sin \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)\sqrt{3}+9\sqrt[3]{44+12\sqrt{69}}\sqrt{69}\cos \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)-11\sqrt[3]{44+12\sqrt{69}}\sqrt{3}\sin \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)-33\sqrt[3]{44+12\sqrt{69}}\cos \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)+100\sin \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)\sqrt{3}-300\cos \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right))\mathrm{d}x{x}^{\frac{\sqrt[3]{44+12\sqrt{69}}}{12}+\frac{2}{3}+\frac{11{(44+12\sqrt{69})}^{2/3}}{1200}-\frac{\sqrt{69}{(44+12\sqrt{69})}^{\frac{2}{3}}}{400}}\sin \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)+\mathit{\_}\mathit{C}\mathit{1}{x}^{\frac{\sqrt{69}{(44+12\sqrt{69})}^{\frac{2}{3}}}{200}-\frac{11{(44+12\sqrt{69})}^{2/3}}{600}-\frac{\sqrt[3]{44+12\sqrt{69}}}{6}+\frac{2}{3}}+\mathit{\_}\mathit{C}\mathit{2}{x}^{\frac{\sqrt[3]{44+12\sqrt{69}}}{12}+\frac{2}{3}+\frac{11{(44+12\sqrt{69})}^{2/3}}{1200}-\frac{\sqrt{69}{(44+12\sqrt{69})}^{\frac{2}{3}}}{400}}\cos \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)+\mathit{\_}\mathit{C}\mathit{3}{x}^{\frac{\sqrt[3]{44+12\sqrt{69}}}{12}+\frac{2}{3}+\frac{11{(44+12\sqrt{69})}^{2/3}}{1200}-\frac{\sqrt{69}{(44+12\sqrt{69})}^{\frac{2}{3}}}{400}}\sin \left(\frac{\sqrt[3]{44+12\sqrt{69}}\sqrt{3}(3\sqrt[3]{44+12\sqrt{69}}\sqrt{69}-11\sqrt[3]{44+12\sqrt{69}}+100)\ln \left(x\right)}{1200}\right)\}$$