2.1169   ODE No. 1169

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

$$y(x)(ax-b^2)+x^2{y}^{″}(x)+2x{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0547821 (sec), leaf count = 236

$$\left\{\{y(x)\to c_1{a}^{\frac{1}{2}(-\sqrt{4b^2+1}-1)+\frac{1}{2}\sqrt{4b^2+1}}{x}^{\frac{1}{2}(-\sqrt{4b^2+1}-1)+\frac{1}{2}\sqrt{4b^2+1}}\mathrm{\Gamma }(1-\sqrt{4b^2+1})J_{-\sqrt{4b^2+1}}\left(2\sqrt{a}\sqrt{x}\right)+c_2{a}^{\frac{1}{2}(\sqrt{4b^2+1}-1)-\frac{1}{2}\sqrt{4b^2+1}}{x}^{\frac{1}{2}(\sqrt{4b^2+1}-1)-\frac{1}{2}\sqrt{4b^2+1}}\mathrm{\Gamma }(\sqrt{4b^2+1}+1)J_{\sqrt{4b^2+1}}\left(2\sqrt{a}\sqrt{x}\right)\}\right\}$$ ✓ Maple : cpu = 0.197 (sec), leaf count = 49

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