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 = 0.162704 (sec), leaf count = 33
\[\left \{\left \{y(x)\to \frac {\log (x)+1}{4 x}+\frac {c_1}{x}+c_2 x+c_3 x \log (x)\right \}\right \}\]
Maple ✓
cpu = 0.072 (sec), leaf count = 27
\[\left [y \left (x \right ) = \frac {1+\ln \left (x \right )}{4 x}+\textit {\_C1} x +\frac {\textit {\_C2}}{x}+\textit {\_C3} x \ln \left (x \right )\right ]\] 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))
Maple raw output
[y(x) = 1/4/x*(1+ln(x))+_C1*x+_C2/x+_C3*x*ln(x)]