ODE
\[ x^2 y''(x)+3 x y'(x)+y(x)=x \] ODE Classification
[[_2nd_order, _exact, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00960758 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {4 c_2 \log (x)+4 c_1+x^2}{4 x}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 20
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C2}}{x}}+{\frac {x}{4}}+{\frac {{\it \_C1}\,\ln \left ( x \right ) }{x}} \right \} \] Mathematica raw input
DSolve[y[x] + 3*x*y'[x] + x^2*y''[x] == x,y[x],x]
Mathematica raw output
{{y[x] -> (x^2 + 4*C[1] + 4*C[2]*Log[x])/(4*x)}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)+y(x) = x, y(x),'implicit')
Maple raw output
y(x) = _C2/x+1/4*x+1/x*_C1*ln(x)