\[ (a x+b) y'(x)+c y(x)+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.14887 (sec), leaf count = 266
DSolve[c*y[x] + (b + a*x)*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 i^{-\sqrt {a^2-2 a-4 c+1}+a-1} b^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 c+1}+a-1\right )} \left (\frac {1}{x}\right )^{\frac {1}{2} \left (-\sqrt {a^2-2 a-4 c+1}+a-1\right )} \, _1F_1\left (\frac {a}{2}-\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2};1-\sqrt {a^2-2 a-4 c+1};\frac {b}{x}\right )+c_2 i^{\sqrt {a^2-2 a-4 c+1}+a-1} b^{\frac {1}{2} \left (\sqrt {a^2-2 a-4 c+1}+a-1\right )} \left (\frac {1}{x}\right )^{\frac {1}{2} \left (\sqrt {a^2-2 a-4 c+1}+a-1\right )} \, _1F_1\left (\frac {a}{2}+\frac {1}{2} \sqrt {a^2-2 a-4 c+1}-\frac {1}{2};\sqrt {a^2-2 a-4 c+1}+1;\frac {b}{x}\right )\right \}\right \}\] ✓ Maple : cpu = 0.157 (sec), leaf count = 114
dsolve(x^2*diff(diff(y(x),x),x)+(a*x+b)*diff(y(x),x)+c*y(x)=0,y(x))
\[y \left (x \right ) = x^{-\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}-\frac {a}{2}+\frac {1}{2}} \left (\KummerM \left (-\frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}, 1+\sqrt {a^{2}-2 a -4 c +1}, \frac {b}{x}\right ) c_{1}+\KummerU \left (-\frac {1}{2}+\frac {\sqrt {a^{2}-2 a -4 c +1}}{2}+\frac {a}{2}, 1+\sqrt {a^{2}-2 a -4 c +1}, \frac {b}{x}\right ) c_{2}\right )\]