ODE
\[ x^4 y''(x)-2 x^2 y'(x)+(2 x+1) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0211511 (sec), leaf count = 20
\[\left \{\left \{y(x)\to e^{-1/x} \left (c_2 x+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.045 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{x}^{-1}}} \left ( {\it \_C2}\,x+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[(1 + 2*x)*y[x] - 2*x^2*y'[x] + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x*C[2])/E^x^(-1)}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)-2*x^2*diff(y(x),x)+(1+2*x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(-1/x)*(_C2*x+_C1)