4.177   ODE No. 1177

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

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

Mathematica: cpu = 174.646177 (sec), leaf count = 136 $$\left\{\{y(x)\to c_2{\int }_1^x{e}^{\frac{2}{K[1]}-K[1]}K[1{]}^{2}dK[1]+{\int }_1^x-\frac{e^{K[2]-\frac{2}{K[2]}}\sec (K[2])({\int }_1^{K[2]}{e}^{\frac{2}{K[1]}-K[1]}K[1{]}^{2}dK[1])}{K[2{]}^2}dK[2]+({\int }_1^x{e}^{\frac{2}{K[1]}-K[1]}K[1{]}^{2}dK[1]){\int }_1^x\frac{e^{K[3]-\frac{2}{K[3]}}\sec (K[3])}{K[3{]}^2}dK[3]+c_1\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 39 $$\{y\left(x\right)=x\sin \left(x\right)\mathit{\_}\mathit{C}\mathit{2}+\cos \left(x\right)x\mathit{\_}\mathit{C}\mathit{1}+x(\ln \left(x\right)\sin \left(x\right)-\int \frac{\sin \left(x\right)}{\cos \left(x\right)x}\mathrm{d}x\cos \left(x\right))\}$$