4.28.23 $a{y}^{\prime }(x)+bxy(x)+x{y}^{″}(x)=0$

ODE
$$a{y}^{\prime }(x)+bxy(x)+x{y}^{″}(x)=0$$ ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0225325 (sec), leaf count = 54

$$\left\{\{y(x)\to x^{\frac{1}{2}-\frac{a}{2}}(c_1{J}_{\frac{a-1}{2}}\left(\sqrt{b}x\right)+c_2{Y}_{\frac{a-1}{2}}\left(\sqrt{b}x\right))\}\right\}$$

Maple ✓
cpu = 0.043 (sec), leaf count = 39

$$\{y\left(x\right)=x^{-\frac{a}{2}+\frac{1}{2}}({\mathit{Y}}_{\frac{a}{2}-\frac{1}{2}}\left(\sqrt{b}x\right)\mathit{\_}\mathit{C}\mathit{2}+{\mathit{J}}_{\frac{a}{2}-\frac{1}{2}}\left(\sqrt{b}x\right)\mathit{\_}\mathit{C}\mathit{1})\}$$ 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)