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 = 0.168123 (sec), leaf count = 25
\[\left \{\left \{y(x)\to \frac {x^2}{3}+c_2 x+c_1 \sqrt {x}\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 18
\[\left [y \left (x \right ) = \sqrt {x}\, \textit {\_C2} +\textit {\_C1} x +\frac {x^{2}}{3}\right ]\] 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))
Maple raw output
[y(x) = x^(1/2)*_C2+_C1*x+1/3*x^2]