4.384   ODE No. 1384

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)=-1/4\frac{(-x^2(a^2-1)+2(a+3)bx-b^2)y\left(x\right)}{x^2}=0}}$$

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

Mathematica: cpu = 0.033504 (sec), leaf count = 110 $$\left\{\{y(x)\to c_1{M}_{\frac{(a+3)b}{2\sqrt{a^2-1}},\frac{\sqrt{b(b^2+1)}}{2\sqrt{b}}}\left(\sqrt{a^2-1}x\right)+c_2{W}_{\frac{(a+3)b}{2\sqrt{a^2-1}},\frac{\sqrt{b(b^2+1)}}{2\sqrt{b}}}\left(\sqrt{a^2-1}x\right)\}\right\}$$

Maple: cpu = 0.187 (sec), leaf count = 73 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathit{M}}_{\frac{(a+3)b}{2}\frac{1}{\sqrt{a^2-1}},\frac{1}{2}\sqrt{b^2+1}}\left(\sqrt{a^2-1}x\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathit{W}}_{\frac{(a+3)b}{2}\frac{1}{\sqrt{a^2-1}},\frac{1}{2}\sqrt{b^2+1}}\left(\sqrt{a^2-1}x\right)\}$$