ODE
\[ x^2 y''(x)+x y'(x)-y(x)=a x^2 \] ODE Classification
[[_2nd_order, _exact, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.164616 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \frac {a x^2}{3}+c_2 x+\frac {c_1}{x}\right \}\right \}\]
Maple ✓
cpu = 0.146 (sec), leaf count = 19
\[\left [y \left (x \right ) = \textit {\_C2} x +\frac {a \,x^{2}}{3}+\frac {\textit {\_C1}}{x}\right ]\] Mathematica raw input
DSolve[-y[x] + x*y'[x] + x^2*y''[x] == a*x^2,y[x],x]
Mathematica raw output
{{y[x] -> (a*x^2)/3 + C[1]/x + x*C[2]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x) = a*x^2, y(x))
Maple raw output
[y(x) = _C2*x+1/3*a*x^2+1/x*_C1]