\[ (a x+b) y'(x)+y(x) (c x+d)+y''(x)=0 \] ✓ Mathematica : cpu = 0.0339103 (sec), leaf count = 172
DSolve[(d + c*x)*y[x] + (b + a*x)*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{\frac {c x}{a}-\frac {a x^2}{2}-b x} H_{\frac {-a^3+d a^2-b c a+c^2}{a^3}}\left (\frac {a b-2 c}{\sqrt {2} a^{3/2}}+\frac {\sqrt {a} x}{\sqrt {2}}\right )+c_2 e^{\frac {c x}{a}-\frac {a x^2}{2}-b x} \, _1F_1\left (-\frac {-a^3+d a^2-b c a+c^2}{2 a^3};\frac {1}{2};\left (\frac {a b-2 c}{\sqrt {2} a^{3/2}}+\frac {\sqrt {a} x}{\sqrt {2}}\right )^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.044 (sec), leaf count = 98
dsolve(diff(diff(y(x),x),x)+(a*x+b)*diff(y(x),x)+(c*x+d)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {c x}{a}} \left (\KummerU \left (\frac {d \,a^{2}-a b c +c^{2}}{2 a^{3}}, \frac {1}{2}, -\frac {\left (a^{2} x +a b -2 c \right )^{2}}{2 a^{3}}\right ) c_{2}+\KummerM \left (\frac {d \,a^{2}-a b c +c^{2}}{2 a^{3}}, \frac {1}{2}, -\frac {\left (a^{2} x +a b -2 c \right )^{2}}{2 a^{3}}\right ) c_{1}\right )\]