2.1573   ODE No. 1573

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

$$-\frac{1}{x^5}+(2x+e^x)y^{(4)}(x)+4(e^x+2)y^{(3)}(x)+6e^x{y}^{″}(x)+4e^x{y}^{\prime }(x)+e^{x}y(x)=0$$ ✗ Mathematica : cpu = 0.0577987 (sec), leaf count = 0 , could not solve

DSolve[-x^(-5) + E^x*y[x] + 4*E^x*Derivative[1][y][x] + 6*E^x*Derivative[2][y][x] + 4*(2 + E^x)*Derivative[3][y][x] + (E^x + 2*x)*Derivative[4][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.045 (sec), leaf count = 65

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{4}}{{\mathrm{e}}^x+2x}+\frac{\mathit{\_}\mathit{C}\mathit{1}{x}^3}{{\mathrm{e}}^x+2x}+\frac{x^2\mathit{\_}\mathit{C}\mathit{2}}{{\mathrm{e}}^x+2x}+\frac{\mathit{\_}\mathit{C}\mathit{3}x}{{\mathrm{e}}^x+2x}+\frac{1}{(24{\mathrm{e}}^x+48x)x}\}$$