4.376   ODE No. 1376

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

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

Mathematica: cpu = 0.096512 (sec), leaf count = 82 $$\left\{\{y(x)\to c_2\sin \left(\frac{\sqrt{b}(\log (x)-\log (\sqrt{a}\sqrt{a+x^2}+a))}{\sqrt{a}}\right)+c_1\cos \left(\frac{\sqrt{b}(\log (x)-\log (\sqrt{a}\sqrt{a+x^2}+a))}{\sqrt{a}}\right)\}\right\}$$

Maple: cpu = 0.016 (sec), leaf count = 71 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\left({\left(\frac{1}{x}(2a+2\sqrt{a}\sqrt{x^2+a})\right)}^{i\sqrt{b}\frac{1}{\sqrt{a}}}\right)}^{-1}+\mathit{\_}\mathit{C}\mathit{2}{\left(\frac{1}{x}(2a+2\sqrt{a}\sqrt{x^2+a})\right)}^{i\sqrt{b}\frac{1}{\sqrt{a}}}\}$$