8.236   ODE No. 1826

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

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

Mathematica: cpu = 0.773098 (sec), leaf count = 233 $$\{\text{Solve}[\frac{3(ay(x)+b{)}^2(3c_1-\frac{4(ay(x)+b{)}^{3/2}}{a})(1-\frac{4(ay(x)+b{)}^{3/2}}{3a{c}_1}){}_2{F}_1(\frac{1}{2},\frac{2}{3};\frac{5}{3};\frac{4(b+ay(x){)}^{3/2}}{3a{c}_1}){}^2}{(4(ay(x)+b{)}^{3/2}-3a{c}_1){}^2}=(c_2+x){}^2,y(x)],\text{Solve}[\frac{3(ay(x)+b{)}^2(\frac{4(ay(x)+b{)}^{3/2}}{a}+3c_1)(\frac{4(ay(x)+b{)}^{3/2}}{3a{c}_1}+1){}_2{F}_1(\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{4(b+ay(x){)}^{3/2}}{3a{c}_1}){}^2}{(4(ay(x)+b{)}^{3/2}+3a{c}_1){}^2}=(c_2+x){}^2,y(x)]\}$$

Maple: cpu = 0.203 (sec), leaf count = 201 $$\{{\int }^{y\left(x\right)}a\sqrt{3}\frac{1}{\sqrt{a(4\mathit{\_}\mathit{a}\sqrt{a\mathit{\_}\mathit{a}+b}a+4b\sqrt{a\mathit{\_}\mathit{a}+b}-\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-3\frac{a}{\sqrt{-3a(4\mathit{\_}\mathit{a}\sqrt{a\mathit{\_}\mathit{a}+b}a+4b\sqrt{a\mathit{\_}\mathit{a}+b}-\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}3\frac{a}{\sqrt{-3a(4\mathit{\_}\mathit{a}\sqrt{a\mathit{\_}\mathit{a}+b}a+4b\sqrt{a\mathit{\_}\mathit{a}+b}-\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-a\sqrt{3}\frac{1}{\sqrt{a(4\mathit{\_}\mathit{a}\sqrt{a\mathit{\_}\mathit{a}+b}a+4b\sqrt{a\mathit{\_}\mathit{a}+b}-\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,y\left(x\right)=-\frac{b}{a}\}$$