2.1037   ODE No. 1037

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

✓ Mathematica : cpu = 0.0161222 (sec), leaf count = 101

DSolve[(-c - b^2*x^2)*y[x] + a*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{-\frac {a x}{2}-\frac {b x^2}{2}} H_{\frac {-a^2-4 b-4 c}{8 b}}\left (\sqrt {b} x\right )+c_2 e^{-\frac {a x}{2}-\frac {b x^2}{2}} \, _1F_1\left (-\frac {-a^2-4 b-4 c}{16 b};\frac {1}{2};b x^2\right )\right \}\right \}\]

✓ Maple : cpu = 0.182 (sec), leaf count = 64

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

\[y \left (x \right ) = {\mathrm e}^{-\frac {x \left (b x +a \right )}{2}} x \left (\operatorname {KummerU}\left (\frac {a^{2}+12 b +4 c}{16 b}, \frac {3}{2}, b \,x^{2}\right ) c_{2} +\operatorname {KummerM}\left (\frac {a^{2}+12 b +4 c}{16 b}, \frac {3}{2}, b \,x^{2}\right ) c_{1} \right )\]