2.1277   ODE No. 1277

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

$$-(a{x}^2+1)y(x)+4x^2{y}^{″}(x)+4x{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0264569 (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 = 0.4 (sec), leaf count = 29

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sinh \left(\frac{x}{2}\sqrt{a}\right)\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{2}\cosh \left(\frac{x}{2}\sqrt{a}\right)\frac{1}{\sqrt{x}}\}$$