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 = 0.00843867 (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 = 0.053 (sec), leaf count = 49
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {ax}{2}}}} \left ( {{\rm Bi}\left ({\frac {{a}^{2}-4\,cx-4\,b}{4}{c}^{-{\frac {2}{3}}}}\right )}{\it \_C2}+{{\rm Ai}\left ({\frac {{a}^{2}-4\,cx-4\,b}{4}{c}^{-{\frac {2}{3}}}}\right )}{\it \_C1} \right ) \right \} \] 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),'implicit')
Maple raw output
y(x) = exp(-1/2*a*x)*(AiryBi(1/4*(a^2-4*c*x-4*b)/c^(2/3))*_C2+AiryAi(1/4*(a^2-4*c*x-4*b)/c^(2/3))*_C1)