4.277   ODE No. 1277

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

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

Mathematica: cpu = 0.028504 (sec), leaf count = 51 $$\left\{\{y(x)\to \frac{c_1{e}^{-\frac{\sqrt{a}x}{2}}}{\sqrt{x}}+\frac{c_2{e}^{\frac{\sqrt{a}x}{2}}}{\sqrt{a}\sqrt{x}}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 29 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sinh \left(\frac{x}{2}\sqrt{a}\right)\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{2}\cosh \left(\frac{x}{2}\sqrt{a}\right)\frac{1}{\sqrt{x}}\}$$