3.390   ODE No. 390

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

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

Mathematica: cpu = 1.795728 (sec), leaf count = 142 $$\text{Solve}[\{x=c_1{e}^{b(\frac{\log (\text{K}\mathrm{\$}\text{1206119})}{b}-\frac{\log (b-a{\text{K}\mathrm{\$}\text{1206119}}^2)}{2b})}+e^{b(\frac{\log (\text{K}\mathrm{\$}\text{1206119})}{b}-\frac{\log (b-a{\text{K}\mathrm{\$}\text{1206119}}^2)}{2b})}(\frac{{\tan }^{-1}\left(\frac{\sqrt{a}\text{K}\mathrm{\$}\text{1206119}}{\sqrt{b-a{\text{K}\mathrm{\$}\text{1206119}}^2}}\right)}{\sqrt{a}}-\frac{c\sqrt{b-a{\text{K}\mathrm{\$}\text{1206119}}^2}}{b\text{K}\mathrm{\$}\text{1206119}}),y(x)=\frac{bx}{a\text{K}\mathrm{\$}\text{1206119}}+\frac{c-{\text{K}\mathrm{\$}\text{1206119}}^2}{a\text{K}\mathrm{\$}\text{1206119}}\},\{y(x),\text{K}\mathrm{\$}\text{1206119}\}]$$

Maple: cpu = 0.655 (sec), leaf count = 416 $$\{y\left(x\right)=2\frac{b{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}b{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}bx+\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}{b}^2-{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{Z}b-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}c+a{b}^{2}x-\mathit{\_}\mathit{Z}{b}^2+abc)}x}{({\mathrm{e}}^{2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}b{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}bx+\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}{b}^2-{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{Z}b-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}c+a{b}^{2}x-\mathit{\_}\mathit{Z}{b}^2+abc)}+b)\sqrt{a}}+2\frac{{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}b{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}bx+\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}{b}^2-{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{Z}b-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}c+a{b}^{2}x-\mathit{\_}\mathit{Z}{b}^2+abc)}}{({\mathrm{e}}^{2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}b{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}bx+\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}{b}^2-{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{Z}b-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}c+a{b}^{2}x-\mathit{\_}\mathit{Z}{b}^2+abc)}+b)\sqrt{a}}(-1/4\frac{{({\mathrm{e}}^{2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}b{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}bx+\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}{b}^2-{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{Z}b-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}c+a{b}^{2}x-\mathit{\_}\mathit{Z}{b}^2+abc)}+b)}^2{\mathrm{e}}^{-2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}b{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}bx+\sqrt{a}\mathit{\_}\mathit{C}\mathit{1}{b}^2-{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{Z}b-a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}c+a{b}^{2}x-\mathit{\_}\mathit{Z}{b}^2+abc)}}{a}+c)\}$$