\[ y(x) \left (\text {a0} x^2+\text {b0} x+\text {c0}\right )+\left (\text {a1} x^2+\text {b1} x\right ) y'(x)+\text {a2} x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.320354 (sec), leaf count = 356
\[\left \{\left \{y(x)\to c_1 U\left (-\frac {2 \text {b0} \text {a2}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {a2}-\text {a1} \text {b1}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \sqrt {\text {a2}^2-2 \text {b1} \text {a2}-4 \text {c0} \text {a2}+\text {b1}^2}}{2 \text {a2} \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}},\frac {\sqrt {\text {a2}^2-2 \text {b1} \text {a2}-4 \text {c0} \text {a2}+\text {b1}^2}}{\text {a2}}+1,\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} x}{\text {a2}}\right ) \exp \left (\frac {\log (x) \left (\sqrt {\text {a2}^2-2 \text {a2} (\text {b1}+2 \text {c0})+\text {b1}^2}+\text {a2}-\text {b1}\right )-x \left (\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}+\text {a1}\right )}{2 \text {a2}}\right )+c_2 L_{\frac {2 \text {b0} \text {a2}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {a2}-\text {a1} \text {b1}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \sqrt {\text {a2}^2-2 \text {b1} \text {a2}-4 \text {c0} \text {a2}+\text {b1}^2}}{2 \text {a2} \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}}^{\frac {\sqrt {\text {a2}^2-2 \text {b1} \text {a2}-4 \text {c0} \text {a2}+\text {b1}^2}}{\text {a2}}}\left (\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} x}{\text {a2}}\right ) \exp \left (\frac {\log (x) \left (\sqrt {\text {a2}^2-2 \text {a2} (\text {b1}+2 \text {c0})+\text {b1}^2}+\text {a2}-\text {b1}\right )-x \left (\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}+\text {a1}\right )}{2 \text {a2}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.312 (sec), leaf count = 150
\[y \relax (x ) = x^{-\frac {\mathit {b1}}{2 \mathit {a2}}} {\mathrm e}^{-\frac {\mathit {a1} x}{2 \mathit {a2}}} \left (\WhittakerW \left (-\frac {\mathit {a1} \mathit {b1} -2 \mathit {a2} \mathit {b0}}{2 \mathit {a2} \sqrt {-4 \mathit {a0} \mathit {a2} +\mathit {a1}^{2}}}, \frac {\sqrt {\mathit {a2}^{2}+\left (-2 \mathit {b1} -4 \mathit {c0} \right ) \mathit {a2} +\mathit {b1}^{2}}}{2 \mathit {a2}}, \frac {\sqrt {-4 \mathit {a0} \mathit {a2} +\mathit {a1}^{2}}\, x}{\mathit {a2}}\right ) c_{2}+\WhittakerM \left (-\frac {\mathit {a1} \mathit {b1} -2 \mathit {a2} \mathit {b0}}{2 \mathit {a2} \sqrt {-4 \mathit {a0} \mathit {a2} +\mathit {a1}^{2}}}, \frac {\sqrt {\mathit {a2}^{2}+\left (-2 \mathit {b1} -4 \mathit {c0} \right ) \mathit {a2} +\mathit {b1}^{2}}}{2 \mathit {a2}}, \frac {\sqrt {-4 \mathit {a0} \mathit {a2} +\mathit {a1}^{2}}\, x}{\mathit {a2}}\right ) c_{1}\right )\]