ODE
\[ 2 x^2 y''(x)-x y'(x)+y(x)=x^2 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0247336 (sec), leaf count = 25
\[\left \{\left \{y(x)\to c_2 x+c_1 \sqrt {x}+\frac {x^2}{3}\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) =x{\it \_C2}+\sqrt {x}{\it \_C1}+{\frac {{x}^{2}}{3}} \right \} \] Mathematica raw input
DSolve[y[x] - x*y'[x] + 2*x^2*y''[x] == x^2,y[x],x]
Mathematica raw output
{{y[x] -> x^2/3 + Sqrt[x]*C[1] + x*C[2]}}
Maple raw input
dsolve(2*x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = x^2, y(x),'implicit')
Maple raw output
y(x) = x*_C2+x^(1/2)*_C1+1/3*x^2