ODE
\[ a y'(x)+y(x) (\text {b1}+\text {b2} x)+x y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0817264 (sec), leaf count = 85
\[\left \{\left \{y(x)\to e^{-i \sqrt {\text {b2}} x} \left (c_1 U\left (\frac {1}{2} \left (a+\frac {i \text {b1}}{\sqrt {\text {b2}}}\right ),a,2 i \sqrt {\text {b2}} x\right )+c_2 L_{-\frac {a}{2}-\frac {i \text {b1}}{2 \sqrt {\text {b2}}}}^{a-1}\left (2 i \sqrt {\text {b2}} x\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.184 (sec), leaf count = 66
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-i\sqrt {{\it b2}}x}} \left ( {{\sl U}\left ({\frac {1}{2} \left ( a\sqrt {{\it b2}}+i{\it b1} \right ) {\frac {1}{\sqrt {{\it b2}}}}},\,a,\,2\,i\sqrt {{\it b2}}x\right )}{\it \_C2}+{{\sl M}\left ({\frac {1}{2} \left ( a\sqrt {{\it b2}}+i{\it b1} \right ) {\frac {1}{\sqrt {{\it b2}}}}},\,a,\,2\,i\sqrt {{\it b2}}x\right )}{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[(b1 + b2*x)*y[x] + a*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1]*HypergeometricU[(a + (I*b1)/Sqrt[b2])/2, a, (2*I)*Sqrt[b2]*x] + C[2]*LaguerreL[-a/2 - ((I/2)*b1)/Sqrt[b2], -1 + a, (2*I)*Sqrt[b2]*x])/E^(I*Sqrt[b2]*x)}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+a*diff(y(x),x)+(b2*x+b1)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = exp(-I*b2^(1/2)*x)*(KummerU(1/2*(a*b2^(1/2)+I*b1)/b2^(1/2),a,2*I*b2^(1/2)*x)*_C2+KummerM(1/2*(a*b2^(1/2)+I*b1)/b2^(1/2),a,2*I*b2^(1/2)*x)*_C1)