ODE
\[ -2 a \left (1-2 a x^2\right ) y(x)-4 a x y'(x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0157116 (sec), leaf count = 20
\[\left \{\left \{y(x)\to e^{a x^2} \left (c_2 x+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.077 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={{\rm e}^{a{x}^{2}}} \left ( {\it \_C2}\,x+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[-2*a*(1 - 2*a*x^2)*y[x] - 4*a*x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(a*x^2)*(C[1] + x*C[2])}}
Maple raw input
dsolve(diff(diff(y(x),x),x)-4*a*x*diff(y(x),x)-2*a*(-2*a*x^2+1)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(a*x^2)*(_C2*x+_C1)