ODE
\[ a y'(x)+y(x) (b+c x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.157911 (sec), leaf count = 67
\[\left \{\left \{y(x)\to e^{-\frac {a x}{2}} \left (c_1 \text {Ai}\left (\frac {a^2-4 (b+c x)}{4 (-c)^{2/3}}\right )+c_2 \text {Bi}\left (\frac {a^2-4 (b+c x)}{4 (-c)^{2/3}}\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.11 (sec), leaf count = 53
\[\left [y \left (x \right ) = \textit {\_C1} \,{\mathrm e}^{-\frac {a x}{2}} \AiryAi \left (\frac {a^{2}-4 c x -4 b}{4 c^{\frac {2}{3}}}\right )+\textit {\_C2} \,{\mathrm e}^{-\frac {a x}{2}} \AiryBi \left (\frac {a^{2}-4 c x -4 b}{4 c^{\frac {2}{3}}}\right )\right ]\] Mathematica raw input
DSolve[(b + c*x)*y[x] + a*y'[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (AiryAi[(a^2 - 4*(b + c*x))/(4*(-c)^(2/3))]*C[1] + AiryBi[(a^2 - 4*(b + c*x))/(4*(-c)^(2/3))]*C[2])/E^((a*x)/2)}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+a*diff(y(x),x)+(c*x+b)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*exp(-1/2*a*x)*AiryAi(1/4*(a^2-4*c*x-4*b)/c^(2/3))+_C2*exp(-1/2*a*x)*AiryBi(1/4*(a^2-4*c*x-4*b)/c^(2/3))]