ODE
\[ x^4 y'''(x)+2 x^3 y''(x)-x^2 y'(x)+x y(x)=1 \] ODE Classification
[[_3rd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0174024 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {c_1}{x}+c_2 x+c_3 x \log (x)+\frac {\log (x)+1}{4 x}\right \}\right \}\]
Maple ✓
cpu = 0.021 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) ={\frac {4\,{\it \_C3}\,{x}^{2}\ln \left ( x \right ) +4\,{\it \_C1}\,{x}^{2}+\ln \left ( x \right ) +4\,{\it \_C2}+1}{4\,x}} \right \} \] Mathematica raw input
DSolve[x*y[x] - x^2*y'[x] + 2*x^3*y''[x] + x^4*y'''[x] == 1,y[x],x]
Mathematica raw output
{{y[x] -> C[1]/x + x*C[2] + x*C[3]*Log[x] + (1 + Log[x])/(4*x)}}
Maple raw input
dsolve(x^4*diff(diff(diff(y(x),x),x),x)+2*x^3*diff(diff(y(x),x),x)-x^2*diff(y(x),x)+x*y(x) = 1, y(x),'implicit')
Maple raw output
y(x) = 1/4*(4*_C3*x^2*ln(x)+4*_C1*x^2+ln(x)+4*_C2+1)/x