ODE
\[ y(x) (a+b x)+y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.148082 (sec), leaf count = 42
\[\left \{\left \{y(x)\to c_1 \text {Ai}\left (-\frac {a+b x}{(-b)^{2/3}}\right )+c_2 \text {Bi}\left (-\frac {a+b x}{(-b)^{2/3}}\right )\right \}\right \}\]
Maple ✓
cpu = 0.068 (sec), leaf count = 31
\[\left [y \left (x \right ) = \textit {\_C1} \AiryAi \left (-\frac {b x +a}{b^{\frac {2}{3}}}\right )+\textit {\_C2} \AiryBi \left (-\frac {b x +a}{b^{\frac {2}{3}}}\right )\right ]\] Mathematica raw input
DSolve[(a + b*x)*y[x] + y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> AiryAi[-((a + b*x)/(-b)^(2/3))]*C[1] + AiryBi[-((a + b*x)/(-b)^(2/3))]*C[2]}}
Maple raw input
dsolve(diff(diff(y(x),x),x)+(b*x+a)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*AiryAi(-1/b^(2/3)*(b*x+a))+_C2*AiryBi(-1/b^(2/3)*(b*x+a))]