4.28.23 \(a y'(x)+b x y(x)+x y''(x)=0\)

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 = 0.173115 (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 = 0.053 (sec), leaf count = 45

\[\left [y \left (x \right ) = \textit {\_C1} \,x^{-\frac {a}{2}+\frac {1}{2}} \BesselJ \left (\frac {a}{2}-\frac {1}{2}, x \sqrt {b}\right )+\textit {\_C2} \,x^{-\frac {a}{2}+\frac {1}{2}} \BesselY \left (\frac {a}{2}-\frac {1}{2}, x \sqrt {b}\right )\right ]\] 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))

Maple raw output

[y(x) = _C1*x^(-1/2*a+1/2)*BesselJ(1/2*a-1/2,x*b^(1/2))+_C2*x^(-1/2*a+1/2)*Besse
lY(1/2*a-1/2,x*b^(1/2))]