ODE
\[ x^4 y''(x)+x^3 y'(x)-(x+1) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.19673 (sec), leaf count = 24
\[\left \{\left \{y(x)\to e^{\frac {1}{x}} \left (c_1-c_2 \text {Ei}\left (-\frac {2}{x}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.061 (sec), leaf count = 24
\[\left [y \left (x \right ) = {\mathrm e}^{\frac {1}{x}} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{\frac {1}{x}} \expIntegral \left (1, \frac {2}{x}\right )\right ]\] Mathematica raw input
DSolve[-((1 + x)*y[x]) + x^3*y'[x] + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x^(-1)*(C[1] - C[2]*ExpIntegralEi[-2/x])}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)+x^3*diff(y(x),x)-(x+1)*y(x) = 0, y(x))
Maple raw output
[y(x) = exp(1/x)*_C1+_C2*exp(1/x)*Ei(1,2/x)]