ODE No. 1447

\[ y''(x)=-\frac {(-x-1) y(x)}{x^4}-\frac {y'(x)}{x} \] Mathematica : cpu = 0.039288 (sec), leaf count = 29

DSolve[Derivative[2][y][x] == -(((-1 - x)*y[x])/x^4) - Derivative[1][y][x]/x,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{x}}-c_2 e^{\frac {1}{x}} \text {Ei}\left (-\frac {2}{x}\right )\right \}\right \}\] Maple : cpu = 0.051 (sec), leaf count = 20

dsolve(diff(diff(y(x),x),x) = -1/x*diff(y(x),x)-(-1-x)/x^4*y(x),y(x))
 

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