2.1573   ODE No. 1573

\[ -\frac {1}{x^5}+\left (2 x+e^x\right ) y^{(4)}(x)+4 \left (e^x+2\right ) y^{(3)}(x)+6 e^x y''(x)+4 e^x y'(x)+e^x y(x)=0 \]

✓ Mathematica : cpu = 0.138313 (sec), leaf count = 77

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]
 

\[\left \{\left \{y(x)\to \frac {c_4 x^3}{2 x+e^x}+\frac {c_3 x^2}{2 x+e^x}+\frac {1}{24 \left (2 x+e^x\right ) x}+\frac {c_2 x}{2 x+e^x}+\frac {c_1}{2 x+e^x}\right \}\right \}\]

✓ Maple : cpu = 0.05 (sec), leaf count = 41

dsolve((exp(x)+2*x)*diff(diff(diff(diff(y(x),x),x),x),x)+4*(exp(x)+2)*diff(diff(diff(y(x),x),x),x)+6*exp(x)*diff(diff(y(x),x),x)+4*exp(x)*diff(y(x),x)+y(x)*exp(x)-1/x^5=0,y(x))
 

\[y \left (x \right ) = \frac {24 c_{1} x^{4}+24 c_{2} x^{3}+24 c_{3} x^{2}+24 c_{4} x +1}{24 \left ({\mathrm e}^{x}+2 x \right ) x}\]