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 = 0.164939 (sec), leaf count = 23
\[\left \{\left \{y(x)\to \frac {3 x^3}{4}+c_1 x+c_2 x \log (x)\right \}\right \}\]
Maple ✓
cpu = 0.017 (sec), leaf count = 18
\[\left [y \left (x \right ) = \textit {\_C2} x +x \ln \left (x \right ) \textit {\_C1} +\frac {3 x^{3}}{4}\right ]\] 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))
Maple raw output
[y(x) = _C2*x+x*ln(x)*_C1+3/4*x^3]