\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) - \left ( 4\,{a}^{2}{b}^{2}{x}^{2}{{\rm e}^{2\,b{x}^{2}}}-1 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.780099 (sec), leaf count = 35 \[ \text {DSolve}\left [y(x) \left (1-4 a^2 b^2 x^2 e^{2 b x^2}\right )+y''(x)=0,y(x),x\right ] \]
Maple: cpu = 0.531 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) ={\it DESol} \left ( \left \{ {\frac { {\rm d}^{2}}{{\rm d}{x}^{2}}}{\it \_Y} \left ( x \right ) + \left ( -4\,{ a}^{2}{b}^{2}{x}^{2}{{\rm e}^{2\,b{x}^{2}}}+1 \right ) {\it \_Y} \left ( x \right ) \right \} , \left \{ {\it \_Y} \left ( x \right ) \right \} \right ) \right \} \]