\[ y(x) (\text {a0} x+\text {b0})+(\text {a1} x+\text {b1}) y'(x)+(\text {a2} x+\text {b2}) y''(x)=0 \] ✓ Mathematica : cpu = 0.184797 (sec), leaf count = 386
DSolve[(b0 + a0*x)*y[x] + (b1 + a1*x)*Derivative[1][y][x] + (b2 + a2*x)*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \operatorname {HypergeometricU}\left (-\frac {\text {b2} \text {a1}^2-\text {a2} \text {b1} \text {a1}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b2} \text {a1}+2 \text {a2}^2 \text {b0}+\text {a2} \sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b1}-2 \text {a0} \text {a2} \text {b2}-2 \text {a2}^2 \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}{2 \text {a2}^2 \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}},\frac {\text {a2}^2-\text {b1} \text {a2}+\text {a1} \text {b2}}{\text {a2}^2}+1,\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b2}}{\text {a2}^2}+\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} x}{\text {a2}}\right ) \exp \left (\frac {2 \left (\frac {\text {a1} \text {b2}}{\text {a2}}+\text {a2}-\text {b1}\right ) \log (\text {a2} x+\text {b2})-x \left (\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}+\text {a1}\right )}{2 \text {a2}}\right )+c_2 L_{\frac {\text {b2} \text {a1}^2-\text {a2} \text {b1} \text {a1}-\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b2} \text {a1}+2 \text {a2}^2 \text {b0}+\text {a2} \sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b1}-2 \text {a0} \text {a2} \text {b2}-2 \text {a2}^2 \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}{2 \text {a2}^2 \sqrt {\text {a1}^2-4 \text {a0} \text {a2}}}}^{\frac {\text {a2}^2-\text {b1} \text {a2}+\text {a1} \text {b2}}{\text {a2}^2}}\left (\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} \text {b2}}{\text {a2}^2}+\frac {\sqrt {\text {a1}^2-4 \text {a0} \text {a2}} x}{\text {a2}}\right ) \exp \left (\frac {2 \left (\frac {\text {a1} \text {b2}}{\text {a2}}+\text {a2}-\text {b1}\right ) \log (\text {a2} x+\text {b2})-x \left (\sqrt {\text {a1}^2-4 \text {a0} \text {a2}}+\text {a1}\right )}{2 \text {a2}}\right )\right \}\right \}\] ✓ Maple : cpu = 0.194 (sec), leaf count = 248
dsolve((a2*x+b2)*diff(diff(y(x),x),x)+(a1*x+b1)*diff(y(x),x)+(a0*x+b0)*y(x)=0,y(x))
\[y \left (x \right ) = {\mathrm e}^{-\frac {\left (\sqrt {-4 \operatorname {a0} \operatorname {a2} +\operatorname {a1}^{2}}+\operatorname {a1} \right ) x}{2 \operatorname {a2}}} \left (\operatorname {a2} x +\operatorname {b2} \right )^{\frac {\operatorname {a1} \operatorname {b2} +\operatorname {a2}^{2}-\operatorname {a2} \operatorname {b1}}{\operatorname {a2}^{2}}} \left (\operatorname {KummerM}\left (\frac {\left (\operatorname {a1} \operatorname {b2} +2 \operatorname {a2}^{2}-\operatorname {a2} \operatorname {b1} \right ) \sqrt {-4 \operatorname {a0} \operatorname {a2} +\operatorname {a1}^{2}}-2 \operatorname {a2}^{2} \operatorname {b0} +\left (2 \operatorname {a0} \operatorname {b2} +\operatorname {a1} \operatorname {b1} \right ) \operatorname {a2} -\operatorname {a1}^{2} \operatorname {b2}}{2 \sqrt {-4 \operatorname {a0} \operatorname {a2} +\operatorname {a1}^{2}}\, \operatorname {a2}^{2}}, \frac {\operatorname {a1} \operatorname {b2} +2 \operatorname {a2}^{2}-\operatorname {a2} \operatorname {b1}}{\operatorname {a2}^{2}}, \frac {\sqrt {-4 \operatorname {a0} \operatorname {a2} +\operatorname {a1}^{2}}\, \left (\operatorname {a2} x +\operatorname {b2} \right )}{\operatorname {a2}^{2}}\right ) c_{1}+\operatorname {KummerU}\left (\frac {\left (\operatorname {a1} \operatorname {b2} +2 \operatorname {a2}^{2}-\operatorname {a2} \operatorname {b1} \right ) \sqrt {-4 \operatorname {a0} \operatorname {a2} +\operatorname {a1}^{2}}-2 \operatorname {a2}^{2} \operatorname {b0} +\left (2 \operatorname {a0} \operatorname {b2} +\operatorname {a1} \operatorname {b1} \right ) \operatorname {a2} -\operatorname {a1}^{2} \operatorname {b2}}{2 \sqrt {-4 \operatorname {a0} \operatorname {a2} +\operatorname {a1}^{2}}\, \operatorname {a2}^{2}}, \frac {\operatorname {a1} \operatorname {b2} +2 \operatorname {a2}^{2}-\operatorname {a2} \operatorname {b1}}{\operatorname {a2}^{2}}, \frac {\sqrt {-4 \operatorname {a0} \operatorname {a2} +\operatorname {a1}^{2}}\, \left (\operatorname {a2} x +\operatorname {b2} \right )}{\operatorname {a2}^{2}}\right ) c_{2}\right )\]