\[ \left (2 n+3 x^2-1\right ) y(x)+y''(x)-4 x y'(x)=0 \] ✓ Mathematica : cpu = 0.0070398 (sec), leaf count = 45
DSolve[(-1 + 2*n + 3*x^2)*y[x] - 4*x*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{\frac {x^2}{2}} \operatorname {HermiteH}(n,x)+c_2 e^{\frac {x^2}{2}} \operatorname {Hypergeometric1F1}\left (-\frac {n}{2},\frac {1}{2},x^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.082 (sec), leaf count = 37
dsolve(diff(diff(y(x),x),x)-4*x*diff(y(x),x)+(3*x^2+2*n-1)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{\frac {x^{2}}{2}} x \left (\operatorname {KummerM}\left (-\frac {n}{2}+\frac {1}{2}, \frac {3}{2}, x^{2}\right ) c_{1}+\operatorname {KummerU}\left (-\frac {n}{2}+\frac {1}{2}, \frac {3}{2}, x^{2}\right ) c_{2}\right )\]