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 = 0.027042 (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 = 0.021 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{x}^{-1}}} \left ( {\it Ei} \left ( 1,2\,{x}^{-1} \right ) {\it \_C2}+{\it \_C1} \right ) \right \} \] 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)-(1+x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(1/x)*(Ei(1,2/x)*_C2+_C1)