ODE
\[ x^2 y''(x)-x y'(x)+y(x)=x^2 (x+3) \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0116347 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {1}{4} x \left (4 c_2 \log (x)+4 c_1+x^2+12 x\right )\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={\frac {x \left ( 4\,\ln \left ( x \right ) {\it \_C1}+{x}^{2}+4\,{\it \_C2}+12\,x \right ) }{4}} \right \} \] Mathematica raw input
DSolve[y[x] - x*y'[x] + x^2*y''[x] == x^2*(3 + x),y[x],x]
Mathematica raw output
{{y[x] -> (x*(12*x + x^2 + 4*C[1] + 4*C[2]*Log[x]))/4}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = x^2*(3+x), y(x),'implicit')
Maple raw output
y(x) = 1/4*x*(4*ln(x)*_C1+x^2+4*_C2+12*x)