\[ -y'(x) (a b+c+x)+a y''(x)+y(x) (b (c+x)+d)=0 \] ✓ Mathematica : cpu = 0.0316982 (sec), leaf count = 99
DSolve[(d + b*(c + x))*y[x] - (a*b + c + x)*Derivative[1][y][x] + a*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 e^{b x} H_d\left (\frac {x}{\sqrt {2} \sqrt {a}}-\frac {a b-c}{\sqrt {2} \sqrt {a}}\right )+c_2 e^{b x} \, _1F_1\left (-\frac {d}{2};\frac {1}{2};\left (\frac {x}{\sqrt {2} \sqrt {a}}-\frac {a b-c}{\sqrt {2} \sqrt {a}}\right )^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.043 (sec), leaf count = 58
dsolve(a*diff(diff(y(x),x),x)-(a*b+c+x)*diff(y(x),x)+(b*(x+c)+d)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{b x} \left (\KummerU \left (-\frac {d}{2}, \frac {1}{2}, \frac {\left (a b -c -x \right )^{2}}{2 a}\right ) c_{2}+\KummerM \left (-\frac {d}{2}, \frac {1}{2}, \frac {\left (a b -c -x \right )^{2}}{2 a}\right ) c_{1}\right )\]