4.34.7 $\text{a1}(a+bx)y^{\prime }(x)+(a+bx{)}^2{y}^{″}(x)+\text{a2}y(x)=0$

ODE
$$\text{a1}(a+bx)y^{\prime }(x)+(a+bx{)}^2{y}^{″}(x)+\text{a2}y(x)=0$$ ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0325461 (sec), leaf count = 95

$$\left\{\{y(x)\to (a+bx{)}^{-\frac{\sqrt{\text{a2}}\sqrt{\frac{{\text{a1}}^2-2\text{a1}b-4\text{a2}+b^2}{\text{a2}}}+\text{a1}-b}{2b}}(c_2(a+bx{)}^{\frac{\sqrt{\text{a2}}\sqrt{\frac{{\text{a1}}^2-2\text{a1}b-4\text{a2}+b^2}{\text{a2}}}}{b}}+c_1)\}\right\}$$

Maple ✓
cpu = 0.024 (sec), leaf count = 77

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(x+\frac{a}{b})}^{\frac{1}{2b}(-\mathit{a}\mathit{1}+b+\sqrt{{\mathit{a}\mathit{1}}^2-2\mathit{a}\mathit{1}b+b^2-4\mathit{a}\mathit{2}})}+\mathit{\_}\mathit{C}\mathit{2}{(x+\frac{a}{b})}^{-\frac{1}{2b}(\mathit{a}\mathit{1}-b+\sqrt{{\mathit{a}\mathit{1}}^2-2\mathit{a}\mathit{1}b+b^2-4\mathit{a}\mathit{2}})}\}$$ Mathematica raw input

DSolve[a2*y[x] + a1*(a + b*x)*y'[x] + (a + b*x)^2*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (C[1] + (a + b*x)^((Sqrt[a2]*Sqrt[(a1^2 - 4*a2 - 2*a1*b + b^2)/a2])/b)
*C[2])/(a + b*x)^((a1 - b + Sqrt[a2]*Sqrt[(a1^2 - 4*a2 - 2*a1*b + b^2)/a2])/(2*b
))}}

Maple raw input

dsolve((b*x+a)^2*diff(diff(y(x),x),x)+a1*(b*x+a)*diff(y(x),x)+a2*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*(x+a/b)^(1/2*(-a1+b+(a1^2-2*a1*b+b^2-4*a2)^(1/2))/b)+_C2*(x+a/b)^(-1/
2*(a1-b+(a1^2-2*a1*b+b^2-4*a2)^(1/2))/b)