2.1206   ODE No. 1206

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

$$y(x)(abx+c{x}^2+d)+x(2ax+b)y^{\prime }(x)+x^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.11439 (sec), leaf count = 120

$$\left\{\{y(x)\to c_1{e}^{\frac{1}{2}(-2ax-(b-1)\log (x))}{J}_{\frac{1}{2}\sqrt{b^2-2b-4d+1}}(-i\sqrt{a^2-c}x)+c_2{e}^{\frac{1}{2}(-2ax-(b-1)\log (x))}{Y}_{\frac{1}{2}\sqrt{b^2-2b-4d+1}}(-i\sqrt{a^2-c}x)\}\right\}$$

✓ Maple : cpu = 0.069 (sec), leaf count = 87

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