ODE No. 1013

\[ \left (-a^2 x^2-a\right ) y(x)+y''(x)=0 \]

✓ Mathematica : cpu = 0.0098912 (sec), leaf count = 43

DSolve[(-a - a^2*x^2)*y[x] + Derivative[2][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to c_1 D_{-1}\left (\sqrt {2} \sqrt {a} x\right )+c_2 D_0\left (i \sqrt {2} \sqrt {a} x\right )\right \}\right \}\]

✓ Maple : cpu = 0.056 (sec), leaf count = 22

dsolve(diff(diff(y(x),x),x)-(a^2*x^2+a)*y(x)=0,y(x))

\[y \left (x \right ) = {\mathrm e}^{\frac {a \,x^{2}}{2}} \left (\operatorname {erf}\left (\sqrt {a}\, x \right ) c_{2} +c_{1} \right )\]