\[ y(x) \left (\text {a0} x^2+\text {b0} x+\text {c0}\right )+\left (\text {a1} x^2+\text {b1} x\right ) y'(x)+\text {a2} x^2 y''(x)=0 \] ✓ Mathematica : cpu = 0.212188 (sec), leaf count = 356
DSolve[(c0 + b0*x + a0*x^2)*y[x] + (b1*x + a1*x^2)*Derivative[1][y][x] + a2*x^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \operatorname {HypergeometricU}\left (-\frac {2 \text {b0} \text {a2}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {a2}-\text {a1} \text {b1}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \sqrt {\text {a2}^2-2 \text {b1} \text {a2}-4 \text {c0} \text {a2}+\text {b1}^2}}{2 \text {a2} \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}},\frac {\sqrt {\text {a2}^2-2 \text {b1} \text {a2}-4 \text {c0} \text {a2}+\text {b1}^2}}{\text {a2}}+1,\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} x}{\text {a2}}\right ) \exp \left (\frac {\log (x) \left (\sqrt {\text {a2}^2-2 \text {a2} (\text {b1}+2 \text {c0})+\text {b1}^2}+\text {a2}-\text {b1}\right )-x \left (\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}+\text {a1}\right )}{2 \text {a2}}\right )+c_2 L_{\frac {2 \text {b0} \text {a2}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {a2}-\text {a1} \text {b1}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \sqrt {\text {a2}^2-2 \text {b1} \text {a2}-4 \text {c0} \text {a2}+\text {b1}^2}}{2 \text {a2} \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}}^{\frac {\sqrt {\text {a2}^2-2 \text {b1} \text {a2}-4 \text {c0} \text {a2}+\text {b1}^2}}{\text {a2}}}\left (\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} x}{\text {a2}}\right ) \exp \left (\frac {\log (x) \left (\sqrt {\text {a2}^2-2 \text {a2} (\text {b1}+2 \text {c0})+\text {b1}^2}+\text {a2}-\text {b1}\right )-x \left (\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}+\text {a1}\right )}{2 \text {a2}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.354 (sec), leaf count = 150
dsolve(a2*x^2*diff(diff(y(x),x),x)+(a1*x^2+b1*x)*diff(y(x),x)+(a0*x^2+b0*x+c0)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {\operatorname {a1} x}{2 \operatorname {a2}}} x^{-\frac {\operatorname {b1}}{2 \operatorname {a2}}} \left (\operatorname {WhittakerM}\left (-\frac {\operatorname {a1} \operatorname {b1} -2 \operatorname {a2} \operatorname {b0}}{2 \operatorname {a2} \sqrt {-4 \operatorname {a0} \operatorname {a2} +\operatorname {a1}^{2}}}, \frac {\sqrt {\operatorname {a2}^{2}+\left (-2 \operatorname {b1} -4 \operatorname {c0} \right ) \operatorname {a2} +\operatorname {b1}^{2}}}{2 \operatorname {a2}}, \frac {\sqrt {-4 \operatorname {a0} \operatorname {a2} +\operatorname {a1}^{2}}\, x}{\operatorname {a2}}\right ) c_{1}+\operatorname {WhittakerW}\left (-\frac {\operatorname {a1} \operatorname {b1} -2 \operatorname {a2} \operatorname {b0}}{2 \operatorname {a2} \sqrt {-4 \operatorname {a0} \operatorname {a2} +\operatorname {a1}^{2}}}, \frac {\sqrt {\operatorname {a2}^{2}+\left (-2 \operatorname {b1} -4 \operatorname {c0} \right ) \operatorname {a2} +\operatorname {b1}^{2}}}{2 \operatorname {a2}}, \frac {\sqrt {-4 \operatorname {a0} \operatorname {a2} +\operatorname {a1}^{2}}\, x}{\operatorname {a2}}\right ) c_{2}\right )\]