2.1418   ODE No. 1418

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

$$y^{″}(x)=\frac{y(x)\sin (x)}{x\cos (x)-\sin (x)}-\frac{x\sin (x)y^{\prime }(x)}{x\cos (x)-\sin (x)}$$ ✗ Mathematica : cpu = 1.24282 (sec), leaf count = 0 , could not solve

DSolve[Derivative[2][y][x] == (Sin[x]*y[x])/(x*Cos[x] - Sin[x]) - (x*Sin[x]*Derivative[1][y][x])/(x*Cos[x] - Sin[x]), y[x], x]

✓ Maple : cpu = 17.292 (sec), leaf count = 61

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{2}\sin \left(x\right)\int {\mathrm{e}}^{\int \frac{-2{(\cos \left(x\right))}^{3}x+3{(\cos \left(x\right))}^2\sin \left(x\right)-\sin \left(x\right)}{\cos \left(x\right)(\cos \left(x\right)x-\sin \left(x\right))\sin \left(x\right)}\mathrm{d}x}\cos \left(x\right)\mathrm{d}x\}$$