2.1826   ODE No. 1826

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

$$-ay(x)-b+y^{″}(x{)}^2=0$$ ✓ Mathematica : cpu = 0.72651 (sec), leaf count = 119

$$\{\text{Solve}[\frac{(ay(x)+b{)}^2{}_2{F}_1(\frac{1}{2},\frac{2}{3};\frac{5}{3};-\frac{4(b+ay(x){)}^{3/2}}{3a{c}_1}){}^2}{a^2{c}_1}=(c_2+x){}^2,y(x)],\text{Solve}[\frac{(ay(x)+b{)}^2{}_2{F}_1(\frac{1}{2},\frac{2}{3};\frac{5}{3};\frac{4(b+ay(x){)}^{3/2}}{3a{c}_1}){}^2}{a^2{c}_1}=(c_2+x){}^2,y(x)]\}$$

✓ Maple : cpu = 0.624 (sec), leaf count = 201

$$\{{\int }^{y\left(x\right)}a\sqrt{3}\frac{1}{\sqrt{a(4\mathit{\_}\mathit{a}\sqrt{\mathit{\_}\mathit{a}a+b}a+4b\sqrt{\mathit{\_}\mathit{a}a+b}-\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-3\frac{a}{\sqrt{-3a(4\mathit{\_}\mathit{a}\sqrt{\mathit{\_}\mathit{a}a+b}a+4b\sqrt{\mathit{\_}\mathit{a}a+b}-\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}3\frac{a}{\sqrt{-3a(4\mathit{\_}\mathit{a}\sqrt{\mathit{\_}\mathit{a}a+b}a+4b\sqrt{\mathit{\_}\mathit{a}a+b}-\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-a\sqrt{3}\frac{1}{\sqrt{a(4\mathit{\_}\mathit{a}\sqrt{\mathit{\_}\mathit{a}a+b}a+4b\sqrt{\mathit{\_}\mathit{a}a+b}-\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,y\left(x\right)=-\frac{b}{a}\}$$