2.1842   ODE No. 1842

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

$$x^2{y}^{(3)}(x)+x(y(x)-1)y^{″}(x)+x{y}^{\prime }(x{)}^2+(1-y(x))y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.165997 (sec), leaf count = 286

$$\left\{\{y(x)\to \frac{2x(c_3(J_{\frac{\sqrt{c_2+2}}{\sqrt{2}}}(-\frac{1}{2}ix\sqrt{c_1})-\frac{1}{4}i\sqrt{c_1}x(J_{\frac{\sqrt{c_2+2}}{\sqrt{2}}-1}(-\frac{1}{2}ix\sqrt{c_1})-J_{\frac{\sqrt{c_2+2}}{\sqrt{2}}+1}(-\frac{1}{2}ix\sqrt{c_1})))+Y_{\frac{\sqrt{c_2+2}}{\sqrt{2}}}(-\frac{1}{2}ix\sqrt{c_1})-\frac{1}{4}i\sqrt{c_1}x(Y_{\frac{\sqrt{c_2+2}}{\sqrt{2}}-1}(-\frac{1}{2}ix\sqrt{c_1})-Y_{\frac{\sqrt{c_2+2}}{\sqrt{2}}+1}(-\frac{1}{2}ix\sqrt{c_1})))}{c_{3}x{J}_{\frac{\sqrt{c_2+2}}{\sqrt{2}}}(-\frac{1}{2}ix\sqrt{c_1})+x{Y}_{\frac{\sqrt{c_2+2}}{\sqrt{2}}}(-\frac{1}{2}ix\sqrt{c_1})}\}\right\}$$

✓ Maple : cpu = 0.995 (sec), leaf count = 190

$$\{\ln \left(x\right)+2{\int }^{y\left(x\right)}{(2{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2{\mathit{Y}}_{1/2\sqrt{4+\mathit{\_}\mathit{C}\mathit{1}}}\left(1/2\sqrt{2}\mathit{\_}\mathit{Z}\right)\sqrt{4+\mathit{\_}\mathit{C}\mathit{1}}\mathit{\_}\mathit{C}\mathit{2}+2{\mathit{Y}}_{1/2\sqrt{4+\mathit{\_}\mathit{C}\mathit{1}}}\left(1/2\sqrt{2}\mathit{\_}\mathit{Z}\right)\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{h}+2{\mathit{Y}}_{1/2\sqrt{4+\mathit{\_}\mathit{C}\mathit{1}}+1}\left(1/2\sqrt{2}\mathit{\_}\mathit{Z}\right)\sqrt{2}\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{Z}-4{\mathit{Y}}_{1/2\sqrt{4+\mathit{\_}\mathit{C}\mathit{1}}}\left(1/2\sqrt{2}\mathit{\_}\mathit{Z}\right)\mathit{\_}\mathit{C}\mathit{2}+2{\mathit{J}}_{1/2\sqrt{4+\mathit{\_}\mathit{C}\mathit{1}}+1}\left(1/2\sqrt{2}\mathit{\_}\mathit{Z}\right)\sqrt{2}\mathit{\_}\mathit{Z}-2{\mathit{J}}_{1/2\sqrt{4+\mathit{\_}\mathit{C}\mathit{1}}}\left(1/2\sqrt{2}\mathit{\_}\mathit{Z}\right)\sqrt{4+\mathit{\_}\mathit{C}\mathit{1}}+2{\mathit{J}}_{1/2\sqrt{4+\mathit{\_}\mathit{C}\mathit{1}}}\left(1/2\sqrt{2}\mathit{\_}\mathit{Z}\right)\mathit{\_}\mathit{h}-4{\mathit{J}}_{1/2\sqrt{4+\mathit{\_}\mathit{C}\mathit{1}}}\left(1/2\sqrt{2}\mathit{\_}\mathit{Z}\right))\right)}^2+{\mathit{\_}\mathit{h}}^2-\mathit{\_}\mathit{C}\mathit{1}-4\mathit{\_}\mathit{h})}^{-1}d\mathit{\_}\mathit{h}-\mathit{\_}\mathit{C}\mathit{3}=0\}$$