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 = 0.533342 (sec), leaf count = 133

$$\text{Solve}[c_1=\sqrt[4]{{(\frac{b}{ax}-\frac{1}{a{x}^{2}y(x)})}^2-1}(-\frac{(\frac{b}{ax}-\frac{1}{a{x}^{2}y(x)}){}_2{F}_1(\frac{1}{2},\frac{3}{4};\frac{3}{2};{(\frac{b}{ax}-\frac{1}{a{x}^{2}y(x)})}^2)}{2\sqrt[4]{1-{(\frac{b}{ax}-\frac{1}{a{x}^{2}y(x)})}^2}}-\frac{ax}{b}),y(x)]$$ ✓ Maple : cpu = 0.101 (sec), leaf count = 123

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