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 = 0.176968 (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 = 0.423 (sec), leaf count = 73
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-i \sqrt {\mathit {b2}}\, x} \KummerM \left (\frac {i \mathit {b1} +a \sqrt {\mathit {b2}}}{2 \sqrt {\mathit {b2}}}, a , 2 i \sqrt {\mathit {b2}}\, x \right )+\textit {\_C2} \,{\mathrm e}^{-i \sqrt {\mathit {b2}}\, x} \KummerU \left (\frac {i \mathit {b1} +a \sqrt {\mathit {b2}}}{2 \sqrt {\mathit {b2}}}, a , 2 i \sqrt {\mathit {b2}}\, x \right )\right ]\] 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[-1/2*a - ((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))
Maple raw output
[y(x) = _C1*exp(-I*b2^(1/2)*x)*KummerM(1/2*(I*b1+a*b2^(1/2))/b2^(1/2),a,2*I*b2^(1/2)*x)+_C2*exp(-I*b2^(1/2)*x)*KummerU(1/2*(I*b1+a*b2^(1/2))/b2^(1/2),a,2*I*b2^(1/2)*x)]