2.45   ODE No. 45

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

$$2y(x{)}^3(a^2{x}^3-b^{2}x)+3by(x{)}^2+y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.79557 (sec), leaf count = 120

$$\text{Solve}[\sqrt[4]{\frac{(bxy(x)-1{)}^2}{a^2{x}^{4}y(x{)}^2}-1}(\frac{(bxy(x)-1){}_2{F}_1(\frac{1}{2},\frac{3}{4};\frac{3}{2};\frac{(bxy(x)-1{)}^2}{a^2{x}^{4}y(x{)}^2})}{2a{x}^{2}y(x)\sqrt[4]{1-\frac{(bxy(x)-1{)}^2}{a^2{x}^{4}y(x{)}^2}}}+\frac{ax}{b})+c_1=0,y(x)]$$

✓ Maple : cpu = 0.186 (sec), leaf count = 123

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