ODE
\[ a y'(x)+b x y(x)+x y''(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0225325 (sec), leaf count = 54
\[\left \{\left \{y(x)\to x^{\frac {1}{2}-\frac {a}{2}} \left (c_1 J_{\frac {a-1}{2}}\left (\sqrt {b} x\right )+c_2 Y_{\frac {a-1}{2}}\left (\sqrt {b} x\right )\right )\right \}\right \}\]
Maple ✓
cpu = 0.043 (sec), leaf count = 39
\[ \left \{ y \left ( x \right ) ={x}^{-{\frac {a}{2}}+{\frac {1}{2}}} \left ( {{\sl Y}_{{\frac {a}{2}}-{\frac {1}{2}}}\left (\sqrt {b}x\right )}{\it \_C2}+{{\sl J}_{{\frac {a}{2}}-{\frac {1}{2}}}\left (\sqrt {b}x\right )}{\it \_C1} \right ) \right \} \] Mathematica raw input
DSolve[b*x*y[x] + a*y'[x] + x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^(1/2 - a/2)*(BesselJ[(-1 + a)/2, Sqrt[b]*x]*C[1] + BesselY[(-1 + a)/2, Sqrt[b]*x]*C[2])}}
Maple raw input
dsolve(x*diff(diff(y(x),x),x)+a*diff(y(x),x)+b*x*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x^(-1/2*a+1/2)*(BesselY(1/2*a-1/2,b^(1/2)*x)*_C2+BesselJ(1/2*a-1/2,b^(1/2)*x)*_C1)