2.489   ODE No. 489

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

$$ay(x{)}^2+bx+c+y(x{)}^2{y}^{\prime }(x{)}^2+2xy(x)y^{\prime }(x)=0$$ ✗ Mathematica : cpu = 300.213 (sec), leaf count = 0 , timed out

$Aborted

✓ Maple : cpu = 3.863 (sec), leaf count = 1101

$$\{y\left(x\right)=-\frac{\sqrt{16}}{2a(a+1)}\sqrt{a(a{(a+1)}^2{(ax-\frac{b}{2}+x)}^2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-b\ln (2ax-b+2x)+2{\int }^{\mathit{\_}\mathit{Z}}1/4\frac{b}{(a+1)(4\mathit{\_}\mathit{a}{a}^2+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+a+2)\mathit{\_}\mathit{a}}(-4\mathit{\_}\mathit{a}{a}^2+\sqrt{-(4\mathit{\_}\mathit{a}{a}^3+8\mathit{\_}\mathit{a}{a}^2+4\mathit{\_}\mathit{a}a-1){\mathrm{e}}^{4\frac{a+1}{b}}}{\mathrm{e}}^{-2\frac{a+1}{b}}-8\mathit{\_}\mathit{a}a-4\mathit{\_}\mathit{a}-1)d\mathit{\_}\mathit{a}a+2\mathit{\_}\mathit{C}\mathit{1}a+2{\int }^{\mathit{\_}\mathit{Z}}1/4\frac{b}{(a+1)(4\mathit{\_}\mathit{a}{a}^2+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+a+2)\mathit{\_}\mathit{a}}(-4\mathit{\_}\mathit{a}{a}^2+\sqrt{-(4\mathit{\_}\mathit{a}{a}^3+8\mathit{\_}\mathit{a}{a}^2+4\mathit{\_}\mathit{a}a-1){\mathrm{e}}^{4\frac{a+1}{b}}}{\mathrm{e}}^{-2\frac{a+1}{b}}-8\mathit{\_}\mathit{a}a-4\mathit{\_}\mathit{a}-1)d\mathit{\_}\mathit{a}+2\mathit{\_}\mathit{C}\mathit{1})+(-\frac{bx}{4}-\frac{c}{4})a^2+(-\frac{bx}{4}-\frac{c}{2})a-\frac{b^2}{16}-\frac{c}{4})},y\left(x\right)=\frac{\sqrt{16}}{2a(a+1)}\sqrt{a(a{(a+1)}^2{(ax-\frac{b}{2}+x)}^2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-b\ln (2ax-b+2x)+2{\int }^{\mathit{\_}\mathit{Z}}1/4\frac{b}{(a+1)(4\mathit{\_}\mathit{a}{a}^2+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+a+2)\mathit{\_}\mathit{a}}(-4\mathit{\_}\mathit{a}{a}^2+\sqrt{-(4\mathit{\_}\mathit{a}{a}^3+8\mathit{\_}\mathit{a}{a}^2+4\mathit{\_}\mathit{a}a-1){\mathrm{e}}^{4\frac{a+1}{b}}}{\mathrm{e}}^{-2\frac{a+1}{b}}-8\mathit{\_}\mathit{a}a-4\mathit{\_}\mathit{a}-1)d\mathit{\_}\mathit{a}a+2\mathit{\_}\mathit{C}\mathit{1}a+2{\int }^{\mathit{\_}\mathit{Z}}1/4\frac{b}{(a+1)(4\mathit{\_}\mathit{a}{a}^2+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+a+2)\mathit{\_}\mathit{a}}(-4\mathit{\_}\mathit{a}{a}^2+\sqrt{-(4\mathit{\_}\mathit{a}{a}^3+8\mathit{\_}\mathit{a}{a}^2+4\mathit{\_}\mathit{a}a-1){\mathrm{e}}^{4\frac{a+1}{b}}}{\mathrm{e}}^{-2\frac{a+1}{b}}-8\mathit{\_}\mathit{a}a-4\mathit{\_}\mathit{a}-1)d\mathit{\_}\mathit{a}+2\mathit{\_}\mathit{C}\mathit{1})+(-\frac{bx}{4}-\frac{c}{4})a^2+(-\frac{bx}{4}-\frac{c}{2})a-\frac{b^2}{16}-\frac{c}{4})},y\left(x\right)=-\frac{\sqrt{16}}{2a(a+1)}\sqrt{a(a{(a+1)}^2{(ax-\frac{b}{2}+x)}^2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-b\ln (2ax-b+2x)+2{\int }^{\mathit{\_}\mathit{Z}}-1/4\frac{b}{(a+1)(4\mathit{\_}\mathit{a}{a}^2+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+a+2)\mathit{\_}\mathit{a}}(4\mathit{\_}\mathit{a}{a}^2+\sqrt{-(4\mathit{\_}\mathit{a}{a}^3+8\mathit{\_}\mathit{a}{a}^2+4\mathit{\_}\mathit{a}a-1){\mathrm{e}}^{4\frac{a+1}{b}}}{\mathrm{e}}^{-2\frac{a+1}{b}}+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+1)d\mathit{\_}\mathit{a}a+2\mathit{\_}\mathit{C}\mathit{1}a+2{\int }^{\mathit{\_}\mathit{Z}}-1/4\frac{b}{(a+1)(4\mathit{\_}\mathit{a}{a}^2+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+a+2)\mathit{\_}\mathit{a}}(4\mathit{\_}\mathit{a}{a}^2+\sqrt{-(4\mathit{\_}\mathit{a}{a}^3+8\mathit{\_}\mathit{a}{a}^2+4\mathit{\_}\mathit{a}a-1){\mathrm{e}}^{4\frac{a+1}{b}}}{\mathrm{e}}^{-2\frac{a+1}{b}}+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+1)d\mathit{\_}\mathit{a}+2\mathit{\_}\mathit{C}\mathit{1})+(-\frac{bx}{4}-\frac{c}{4})a^2+(-\frac{bx}{4}-\frac{c}{2})a-\frac{b^2}{16}-\frac{c}{4})},y\left(x\right)=\frac{\sqrt{16}}{2a(a+1)}\sqrt{a(a{(a+1)}^2{(ax-\frac{b}{2}+x)}^2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-b\ln (2ax-b+2x)+2{\int }^{\mathit{\_}\mathit{Z}}-1/4\frac{b}{(a+1)(4\mathit{\_}\mathit{a}{a}^2+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+a+2)\mathit{\_}\mathit{a}}(4\mathit{\_}\mathit{a}{a}^2+\sqrt{-(4\mathit{\_}\mathit{a}{a}^3+8\mathit{\_}\mathit{a}{a}^2+4\mathit{\_}\mathit{a}a-1){\mathrm{e}}^{4\frac{a+1}{b}}}{\mathrm{e}}^{-2\frac{a+1}{b}}+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+1)d\mathit{\_}\mathit{a}a+2\mathit{\_}\mathit{C}\mathit{1}a+2{\int }^{\mathit{\_}\mathit{Z}}-1/4\frac{b}{(a+1)(4\mathit{\_}\mathit{a}{a}^2+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+a+2)\mathit{\_}\mathit{a}}(4\mathit{\_}\mathit{a}{a}^2+\sqrt{-(4\mathit{\_}\mathit{a}{a}^3+8\mathit{\_}\mathit{a}{a}^2+4\mathit{\_}\mathit{a}a-1){\mathrm{e}}^{4\frac{a+1}{b}}}{\mathrm{e}}^{-2\frac{a+1}{b}}+8\mathit{\_}\mathit{a}a+4\mathit{\_}\mathit{a}+1)d\mathit{\_}\mathit{a}+2\mathit{\_}\mathit{C}\mathit{1})+(-\frac{bx}{4}-\frac{c}{4})a^2+(-\frac{bx}{4}-\frac{c}{2})a-\frac{b^2}{16}-\frac{c}{4})}\}$$