2.1170   ODE No. 1170

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

$$y(x)(a{x}^2+b)+x^2{y}^{″}(x)+2x{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.02449 (sec), leaf count = 58

$$\left\{\{y(x)\to c_1{j}_{\frac{1}{2}(\sqrt{1-4b}-1)}\left(\sqrt{a}x\right)+c_2{y}_{\frac{1}{2}(\sqrt{1-4b}-1)}\left(\sqrt{a}x\right)\}\right\}$$

✓ Maple : cpu = 0.036 (sec), leaf count = 45

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{\frac{1}{2}\sqrt{-4b+1}}\left(\sqrt{a}x\right)\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{2}{\mathit{Y}}_{\frac{1}{2}\sqrt{-4b+1}}\left(\sqrt{a}x\right)\frac{1}{\sqrt{x}}\}$$