3.13   ODE No. 13

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

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

Mathematica: cpu = 0.051507 (sec), leaf count = 79 $$\left\{\{y(x)\to -\frac{\sqrt[3]{a}{c}_1{\text{Ai}}^{\prime }\left(\frac{b+ax}{a^{2/3}}\right)+\sqrt[3]{a}{\text{Bi}}^{\prime }\left(\frac{b+ax}{a^{2/3}}\right)}{-c_1\text{Ai}\left(\frac{b+ax}{a^{2/3}}\right)-\text{Bi}\left(\frac{b+ax}{a^{2/3}}\right)}\}\right\}$$

Maple: cpu = 0.125 (sec), leaf count = 79 $$\{y\left(x\right)=-i\sqrt[3]{-ia}({\mathrm{A}\mathrm{i}}^{(1)}(-(ax+b){(-ia)}^{-\frac{2}{3}})\mathit{\_}\mathit{C}\mathit{1}+{\mathrm{B}\mathrm{i}}^{(1)}(-(ax+b){(-ia)}^{-\frac{2}{3}})){(\mathrm{A}\mathrm{i}(-(ax+b){(-ia)}^{-\frac{2}{3}})\mathit{\_}\mathit{C}\mathit{1}+\mathrm{B}\mathrm{i}(-(ax+b){(-ia)}^{-\frac{2}{3}}))}^{-1}\}$$

Sage: cpu = 2.744 (sec), leaf count = 0 $$[[y\left(x\right)=\frac{3a^{5}c{x}^5(4i{\mathrm{I}}_{\frac{4}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+4i{\mathrm{I}}_{\mathrm{-}\frac{2}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a}))+3a^{4}bc{x}^4(20i{\mathrm{I}}_{\frac{4}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+20i{\mathrm{I}}_{\mathrm{-}\frac{2}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a}))+3a^3{b}^{2}c{x}^3(40i{\mathrm{I}}_{\frac{4}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+40i{\mathrm{I}}_{\mathrm{-}\frac{2}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a}))+3a^2{b}^{3}c{x}^2(40i{\mathrm{I}}_{\frac{4}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+40i{\mathrm{I}}_{\mathrm{-}\frac{2}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a}))+3a{b}^{4}cx(20i{\mathrm{I}}_{\frac{4}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+20i{\mathrm{I}}_{\mathrm{-}\frac{2}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a}))+3b^{5}c(4i{\mathrm{I}}_{\frac{4}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+4i{\mathrm{I}}_{\mathrm{-}\frac{2}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a}))+2{\left(\frac{2}{3}\right)}^{\frac{1}{3}}(a^4{x}^2(-9i{\mathrm{Y}}_{\frac{4}{3}}(\frac{2i{(ax+b)}^{\frac{3}{2}}}{3a})+9i{\mathrm{Y}}_{\mathrm{-}\frac{2}{3}}(\frac{2i{(ax+b)}^{\frac{3}{2}}}{3a}))+a^{3}bx(-18i{\mathrm{Y}}_{\frac{4}{3}}(\frac{2i{(ax+b)}^{\frac{3}{2}}}{3a})+18i{\mathrm{Y}}_{\mathrm{-}\frac{2}{3}}(\frac{2i{(ax+b)}^{\frac{3}{2}}}{3a}))+a^2{b}^2(-9i{\mathrm{Y}}_{\frac{4}{3}}(\frac{2i{(ax+b)}^{\frac{3}{2}}}{3a})+9i{\mathrm{Y}}_{\mathrm{-}\frac{2}{3}}(\frac{2i{(ax+b)}^{\frac{3}{2}}}{3a}))+9\sqrt{ax+b}{a}^3{\mathrm{Y}}_{\frac{1}{3}}(\frac{2i{(ax+b)}^{\frac{3}{2}}}{3a})){\left(\frac{{(ax+b)}^{\frac{3}{2}}}{a}\right)}^{\frac{4}{3}}{\left(\frac{2i{(ax+b)}^{\frac{3}{2}}}{3a}\right)}^{\frac{2}{3}}+3(4i{a}^{4}c{x}^3{\mathrm{I}}_{\frac{1}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+12i{a}^{3}bc{x}^2{\mathrm{I}}_{\frac{1}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+12i{a}^2{b}^{2}cx{\mathrm{I}}_{\frac{1}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+4ia{b}^{3}c{\mathrm{I}}_{\frac{1}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a}))\sqrt{ax+b}}{3(12{\left(\frac{2}{3}\right)}^{\frac{1}{3}}(a^{3}x{\mathrm{Y}}_{\frac{1}{3}}(\frac{2i{(ax+b)}^{\frac{3}{2}}}{3a})+a^{2}b{\mathrm{Y}}_{\frac{1}{3}}(\frac{2i{(ax+b)}^{\frac{3}{2}}}{3a}))\sqrt{ax+b}{\left(\frac{{(ax+b)}^{\frac{3}{2}}}{a}\right)}^{\frac{4}{3}}{\left(\frac{2i{(ax+b)}^{\frac{3}{2}}}{3a}\right)}^{\frac{2}{3}}+(8i{a}^{4}c{x}^4{\mathrm{I}}_{\frac{1}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+32i{a}^{3}bc{x}^3{\mathrm{I}}_{\frac{1}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+48i{a}^2{b}^{2}c{x}^2{\mathrm{I}}_{\frac{1}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+32ia{b}^{3}cx{\mathrm{I}}_{\frac{1}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a})+8i{b}^{4}c{\mathrm{I}}_{\frac{1}{3}}(\frac{2{(ax+b)}^{\frac{3}{2}}}{3a}))\sqrt{ax+b})}],\mathtt{\text{riccati}}]$$