ODE
\[ 2 \left (2 x^2+1\right ) y(x)+y''(x)+4 x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0130026 (sec), leaf count = 20
\[\left \{\left \{y(x)\to e^{-x^2} \left (c_2 x+c_1\right )\right \}\right \}\]
Maple ✓
cpu = 0.12 (sec), leaf count = 16
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{x}^{2}}} \left ( {\it \_C2}\,x+{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[2*(1 + 2*x^2)*y[x] + 4*x*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1] + x*C[2])/E^x^2}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+4*x*diff(y(x),x)+2*(2*x^2+1)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(-x^2)*(_C2*x+_C1)