ODE
\[ x^2 y''(x)-x y'(x)+y(x)=3 x^3 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0103605 (sec), leaf count = 23
\[\left \{\left \{y(x)\to c_1 x+c_2 x \log (x)+\frac {3 x^3}{4}\right \}\right \}\]
Maple ✓
cpu = 0.014 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={\frac {x \left ( 4\,\ln \left ( x \right ) {\it \_C1}+3\,{x}^{2}+4\,{\it \_C2} \right ) }{4}} \right \} \] Mathematica raw input
DSolve[y[x] - x*y'[x] + x^2*y''[x] == 3*x^3,y[x],x]
Mathematica raw output
{{y[x] -> (3*x^3)/4 + x*C[1] + x*C[2]*Log[x]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = 3*x^3, y(x),'implicit')
Maple raw output
y(x) = 1/4*x*(4*ln(x)*_C1+3*x^2+4*_C2)