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 = 0.164974 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {1}{4} x \left (x^2+12 x+4 c_2 \log (x)+4 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 23
\[\left [y \left (x \right ) = \textit {\_C2} x +x \ln \left (x \right ) \textit {\_C1} +\frac {x^{3}}{4}+3 x^{2}\right ]\] 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))
Maple raw output
[y(x) = _C2*x+x*ln(x)*_C1+1/4*x^3+3*x^2]