##### 4.25.33 $$\frac {(a+b) y(x)}{x^2}+y''(x)=0$$

ODE
$\frac {(a+b) y(x)}{x^2}+y''(x)=0$ ODE Classiﬁcation

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica
cpu = 0.165195 (sec), leaf count = 61

$\left \{\left \{y(x)\to x^{\frac {1}{2} \left (1-\sqrt {a+b} \sqrt {\frac {1}{a+b}-4}\right )} \left (c_2 x^{\sqrt {a+b} \sqrt {\frac {1}{a+b}-4}}+c_1\right )\right \}\right \}$

Maple
cpu = 0.54 (sec), leaf count = 47

$\left [y \left (x \right ) = \textit {\_C1} \WeierstrassP \left (x , 0, 0\right )^{-\frac {1}{4}-\frac {\sqrt {1-4 a -4 b}}{4}}+\textit {\_C2} \WeierstrassP \left (x , 0, 0\right )^{-\frac {1}{4}+\frac {\sqrt {1-4 a -4 b}}{4}}\right ]$ Mathematica raw input

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

Mathematica raw output

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

Maple raw input

dsolve(diff(diff(y(x),x),x)+(a+b)*WeierstrassP(x,0,0)*y(x) = 0, y(x))

Maple raw output

[y(x) = _C1*WeierstrassP(x,0,0)^(-1/4-1/4*(1-4*a-4*b)^(1/2))+_C2*WeierstrassP(x,
0,0)^(-1/4+1/4*(1-4*a-4*b)^(1/2))]