ODE
\[ x^3 y''(x)+3 x^2 y'(x)+x y(x)=1 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0125748 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {2 c_2 \log (x)+2 c_1+\log ^2(x)}{2 x}\right \}\right \}\]
Maple ✓
cpu = 0.015 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( {\frac { \left ( \ln \left ( x \right ) \right ) ^{2}}{2}}+{\it \_C1}\,\ln \left ( x \right ) +{\it \_C2} \right ) } \right \} \] Mathematica raw input
DSolve[x*y[x] + 3*x^2*y'[x] + x^3*y''[x] == 1,y[x],x]
Mathematica raw output
{{y[x] -> (2*C[1] + 2*C[2]*Log[x] + Log[x]^2)/(2*x)}}
Maple raw input
dsolve(x^3*diff(diff(y(x),x),x)+3*x^2*diff(y(x),x)+x*y(x) = 1, y(x),'implicit')
Maple raw output
y(x) = (1/2*ln(x)^2+_C1*ln(x)+_C2)/x