2.1089   ODE No. 1089

\[ -y'(x) (a b+c+x)+a y''(x)+y(x) (b (c+x)+d)=0 \]

✓ Mathematica : cpu = 0.0243196 (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 = 0.058 (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))
 

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