8.233   ODE No. 1823

$$\boxed{{\displaystyle ({\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+a(x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-y\left(x\right)))\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-b=0}}$$

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

Mathematica: cpu = 0.170022 (sec), leaf count = 35 $$\text{DSolve}[y^{″}(x)(a(x{y}^{\prime }(x)-y(x))+y^{\prime }(x{)}^2)-b=0,y(x),x]$$

Maple: cpu = 0.281 (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}^3-4a{\mathit{\_}\mathit{f}}^{2}b+2a\mathit{\_}\mathit{f}\mathit{\_}\mathit{C}\mathit{1}-\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}{\mathit{\_}\mathit{f}}^2{a}^2+4\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}b\mathit{\_}\mathit{f}-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}^3-4a{\mathit{\_}\mathit{f}}^{2}b+2a\mathit{\_}\mathit{f}\mathit{\_}\mathit{C}\mathit{1}-\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}{\mathit{\_}\mathit{f}}^2{a}^2+4\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}b\mathit{\_}\mathit{f}-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}^3-4a{\mathit{\_}\mathit{f}}^{2}b+2a\mathit{\_}\mathit{f}\mathit{\_}\mathit{C}\mathit{1}+\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}{\mathit{\_}\mathit{f}}^2{a}^2-4\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}b\mathit{\_}\mathit{f}+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}^3-4a{\mathit{\_}\mathit{f}}^{2}b+2a\mathit{\_}\mathit{f}\mathit{\_}\mathit{C}\mathit{1}+\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}{\mathit{\_}\mathit{f}}^2{a}^2-4\sqrt{4\mathit{\_}\mathit{f}b-2\mathit{\_}\mathit{C}\mathit{1}}b\mathit{\_}\mathit{f}+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})\}$$