2.1823   ODE No. 1823

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

$$y^{″}(x)(a(x{y}^{\prime }(x)-y(x))+y^{\prime }(x{)}^2)-b=0$$ ✗ Mathematica : cpu = 0.163469 (sec), leaf count = 0 , could not solve

DSolve[-b + (Derivative[1][y][x]^2 + a*(-y[x] + x*Derivative[1][y][x]))*Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.756 (sec), leaf count = 423

$$\{y\left(x\right)=-\frac{a{x}^2}{4}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x-{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{{\mathit{\_}\mathit{f}}^2{a}^2-4\mathit{\_}\mathit{f}b+2\mathit{\_}\mathit{C}\mathit{1}}\sqrt{{\mathit{\_}\mathit{f}}^3{a}^3-4{\mathit{\_}\mathit{f}}^{2}ab+2\mathit{\_}\mathit{f}a\mathit{\_}\mathit{C}\mathit{1}-\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}{a}^2{\mathit{\_}\mathit{f}}^2+4\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}\mathit{\_}\mathit{f}b-2\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}\mathit{\_}\mathit{C}\mathit{1}}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}),y\left(x\right)=-\frac{a{x}^2}{4}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{{\mathit{\_}\mathit{f}}^2{a}^2-4\mathit{\_}\mathit{f}b+2\mathit{\_}\mathit{C}\mathit{1}}\sqrt{{\mathit{\_}\mathit{f}}^3{a}^3-4{\mathit{\_}\mathit{f}}^{2}ab+2\mathit{\_}\mathit{f}a\mathit{\_}\mathit{C}\mathit{1}-\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}{a}^2{\mathit{\_}\mathit{f}}^2+4\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}\mathit{\_}\mathit{f}b-2\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}\mathit{\_}\mathit{C}\mathit{1}}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}),y\left(x\right)=-\frac{a{x}^2}{4}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x-{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{{\mathit{\_}\mathit{f}}^2{a}^2-4\mathit{\_}\mathit{f}b+2\mathit{\_}\mathit{C}\mathit{1}}\sqrt{{\mathit{\_}\mathit{f}}^3{a}^3-4{\mathit{\_}\mathit{f}}^{2}ab+2\mathit{\_}\mathit{f}a\mathit{\_}\mathit{C}\mathit{1}+\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}{a}^2{\mathit{\_}\mathit{f}}^2-4\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}\mathit{\_}\mathit{f}b+2\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}\mathit{\_}\mathit{C}\mathit{1}}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2}),y\left(x\right)=-\frac{a{x}^2}{4}+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{{\mathit{\_}\mathit{f}}^2{a}^2-4\mathit{\_}\mathit{f}b+2\mathit{\_}\mathit{C}\mathit{1}}\sqrt{{\mathit{\_}\mathit{f}}^3{a}^3-4{\mathit{\_}\mathit{f}}^{2}ab+2\mathit{\_}\mathit{f}a\mathit{\_}\mathit{C}\mathit{1}+\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}{a}^2{\mathit{\_}\mathit{f}}^2-4\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}\mathit{\_}\mathit{f}b+2\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}\mathit{\_}\mathit{C}\mathit{1}}d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{2})\}$$