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 = 0.161024 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {\log ^2(x)+2 c_2 \log (x)+2 c_1}{2 x}\right \}\right \}\]
Maple ✓
cpu = 0.103 (sec), leaf count = 20
\[\left [y \left (x \right ) = \frac {\textit {\_C1} \ln \left (x \right )+\frac {\ln \left (x \right )^{2}}{2}+\textit {\_C2}}{x}\right ]\] 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))
Maple raw output
[y(x) = (_C1*ln(x)+1/2*ln(x)^2+_C2)/x]