\[ -\left (2 a x^2+1\right ) y'(x)+b x^3 y(x)+x y''(x)=0 \] ✓ Mathematica : cpu = 0.0094349 (sec), leaf count = 91
DSolve[b*x^3*y[x] - (1 + 2*a*x^2)*Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{2} \sqrt {b} x^2 \left (\frac {a}{\sqrt {b}}-\frac {\sqrt {a^2-b}}{\sqrt {b}}\right )}+c_2 e^{\frac {1}{2} \sqrt {b} x^2 \left (\frac {\sqrt {a^2-b}}{\sqrt {b}}+\frac {a}{\sqrt {b}}\right )}\right \}\right \}\] ✓ Maple : cpu = 0.058 (sec), leaf count = 45
dsolve(x*diff(diff(y(x),x),x)-(2*a*x^2+1)*diff(y(x),x)+b*x^3*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} {\mathrm e}^{\frac {x^{2} \left (\sqrt {a^{2}-b}+a \right )}{2}}+c_{2} {\mathrm e}^{-\frac {x^{2} \left (\sqrt {a^{2}-b}-a \right )}{2}}\]