ODE
\[ x (\text {a1}+\text {b1} x) y'(x)+\text {a2} y(x)+x^3 y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.102492 (sec), leaf count = 62
\[\left \{\left \{y(x)\to (-1)^{\text {b1}+1} c_2 \text {a1}^{\text {b1}-1} \left (\frac {1}{x}\right )^{\text {b1}-1} \, _1F_1\left (-\frac {\text {a2}}{\text {a1}}+\text {b1}-1;\text {b1};\frac {\text {a1}}{x}\right )+c_1 \, _1F_1\left (-\frac {\text {a2}}{\text {a1}};2-\text {b1};\frac {\text {a1}}{x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.163 (sec), leaf count = 57
\[ \left \{ y \left ( x \right ) ={x}^{-{\it b1}+1} \left ( {{\sl U}\left ({\frac {{\it a1}\, \left ( -1+{\it b1} \right ) -{\it a2}}{{\it a1}}},\,{\it b1},\,{\frac {{\it a1}}{x}}\right )}{\it \_C2}+{{\sl M}\left ({\frac {{\it a1}\, \left ( -1+{\it b1} \right ) -{\it a2}}{{\it a1}}},\,{\it b1},\,{\frac {{\it a1}}{x}}\right )}{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[a2*y[x] + x*(a1 + b1*x)*y'[x] + x^3*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Hypergeometric1F1[-(a2/a1), 2 - b1, a1/x] + (-1)^(1 + b1)*a1^(-1 + b1)*(x^(-1))^(-1 + b1)*C[2]*Hypergeometric1F1[-1 - a2/a1 + b1, b1, a1/x]}}
Maple raw input
dsolve(x^3*diff(diff(y(x),x),x)+x*(b1*x+a1)*diff(y(x),x)+a2*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x^(-b1+1)*(KummerU((a1*(-1+b1)-a2)/a1,b1,1/x*a1)*_C2+KummerM((a1*(-1+b1)-a2)/a1,b1,1/x*a1)*_C1)