4.178   ODE No. 1178

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-2x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+(x^2+2)y\left(x\right)-\frac{x^3}{\cos \left(x\right)}=0}}$$

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

Mathematica: cpu = 0.052507 (sec), leaf count = 74 $$\left\{\{y(x)\to c_1{e}^{-ix}x-\frac{1}{2}i{c}_2{e}^{ix}x+\frac{1}{2}{e}^{-ix}x(e^{2ix}\log (1+e^{-2ix})+\log (1+e^{2ix}))\}\right\}$$

Maple: cpu = 0.016 (sec), leaf count = 28 $$\{y\left(x\right)=x\sin \left(x\right)\mathit{\_}\mathit{C}\mathit{2}+\cos \left(x\right)x\mathit{\_}\mathit{C}\mathit{1}+x(x\sin \left(x\right)+\ln (\cos \left(x\right))\cos \left(x\right))\}$$