ODE
\[ x^3 y(x)-\left (2 x^2+1\right ) y'(x)+x y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0120907 (sec), leaf count = 29
\[\left \{\left \{y(x)\to \frac {1}{2} e^{\frac {x^2}{2}} \left (c_2 x^2+2 c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.035 (sec), leaf count = 18
\[ \left \{ y \left ( x \right ) ={{\rm e}^{{\frac {{x}^{2}}{2}}}} \left ( {\it \_C2}\,{x}^{2}+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[x^3*y[x] - (1 + 2*x^2)*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (E^(x^2/2)*(2*C[1] + x^2*C[2]))/2}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)-(2*x^2+1)*diff(y(x),x)+x^3*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(1/2*x^2)*(_C2*x^2+_C1)