2.1385   ODE No. 1385

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

$$y^{″}(x)=-\frac{(a{x}^2+a-3)y(x)}{4{(x^2+1)}^2}$$ ✓ Mathematica : cpu = 0.0151056 (sec), leaf count = 78

$$\left\{\{y(x)\to c_1\sqrt{x^2+1}{P}_{\frac{1}{2}(\sqrt{1-a}-1)}^{\frac{1}{2}}(ix)+c_2\sqrt{x^2+1}{Q}_{\frac{1}{2}(\sqrt{1-a}-1)}^{\frac{1}{2}}(ix)\}\right\}$$ ✓ Maple : cpu = 0.142 (sec), leaf count = 55

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