ODE
\[ x^2 y''(x)+3 x y'(x)+y(x)=a-x+x \log (x) \] ODE Classification
[[_2nd_order, _exact, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.160067 (sec), leaf count = 33
\[\left \{\left \{y(x)\to a-\frac {x}{2}+\frac {c_1}{x}+\left (\frac {x}{4}+\frac {c_2}{x}\right ) \log (x)\right \}\right \}\]
Maple ✓
cpu = 0.147 (sec), leaf count = 26
\[\left [y \left (x \right ) = \frac {\textit {\_C2}}{x}+\frac {\textit {\_C1} \ln \left (x \right )}{x}-\frac {x}{2}+a +\frac {x \ln \left (x \right )}{4}\right ]\] Mathematica raw input
DSolve[y[x] + 3*x*y'[x] + x^2*y''[x] == a - x + x*Log[x],y[x],x]
Mathematica raw output
{{y[x] -> a - x/2 + C[1]/x + (x/4 + C[2]/x)*Log[x]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)+y(x) = a-x+x*ln(x), y(x))
Maple raw output
[y(x) = _C2/x+1/x*_C1*ln(x)-1/2*x+a+1/4*x*ln(x)]