\[ x (a x+b) y'(x)+y(x) \left (\text {a1} x^2+\text {b1} x+\text {c1}\right )+x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.0796519 (sec), leaf count = 294
DSolve[(c1 + b1*x + a1*x^2)*y[x] + x*(b + a*x)*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 U\left (-\frac {-a b+2 \text {b1}-\sqrt {a^2-4 \text {a1}}-\sqrt {a^2-4 \text {a1}} \sqrt {b^2-2 b-4 \text {c1}+1}}{2 \sqrt {a^2-4 \text {a1}}},\sqrt {b^2-2 b-4 \text {c1}+1}+1,\sqrt {a^2-4 \text {a1}} x\right ) \exp \left (\frac {1}{2} \left (-\left (x \left (\sqrt {a^2-4 \text {a1}}+a\right )\right )-\left (-\sqrt {b^2-2 b-4 \text {c1}+1}+b-1\right ) \log (x)\right )\right )+c_2 L_{\frac {-a b+2 \text {b1}-\sqrt {a^2-4 \text {a1}}-\sqrt {a^2-4 \text {a1}} \sqrt {b^2-2 b-4 \text {c1}+1}}{2 \sqrt {a^2-4 \text {a1}}}}^{\sqrt {b^2-2 b-4 \text {c1}+1}}\left (\sqrt {a^2-4 \text {a1}} x\right ) \exp \left (\frac {1}{2} \left (-\left (x \left (\sqrt {a^2-4 \text {a1}}+a\right )\right )-\left (-\sqrt {b^2-2 b-4 \text {c1}+1}+b-1\right ) \log (x)\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.227 (sec), leaf count = 110
dsolve(x^2*diff(diff(y(x),x),x)+(a*x+b)*diff(y(x),x)*x+(a1*x^2+b1*x+c1)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {a x}{2}} x^{-\frac {b}{2}} \left (\WhittakerW \left (-\frac {a b -2 \mathit {b1}}{2 \sqrt {a^{2}-4 \mathit {a1}}}, \frac {\sqrt {b^{2}-2 b -4 \mathit {c1} +1}}{2}, \sqrt {a^{2}-4 \mathit {a1}}\, x \right ) c_{2}+\WhittakerM \left (-\frac {a b -2 \mathit {b1}}{2 \sqrt {a^{2}-4 \mathit {a1}}}, \frac {\sqrt {b^{2}-2 b -4 \mathit {c1} +1}}{2}, \sqrt {a^{2}-4 \mathit {a1}}\, x \right ) c_{1}\right )\]