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 = 0.162598 (sec), leaf count = 20
\[\left \{\left \{y(x)\to e^{a x^2} (c_2 x+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.075 (sec), leaf count = 22
\[[y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{a \,x^{2}}+\textit {\_C2} \,{\mathrm e}^{a \,x^{2}} x]\] 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))
Maple raw output
[y(x) = _C1*exp(a*x^2)+_C2*exp(a*x^2)*x]