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 = 0.0167078 (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 = 1.219 (sec), leaf count = 47
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( {\it WeierstrassP} \left ( x,0,0 \right ) \right ) ^{-{\frac {1}{4}}-{\frac {1}{4}\sqrt {1-4\,a-4\,b}}}+{\it \_C2}\, \left ( {\it WeierstrassP} \left ( x,0,0 \right ) \right ) ^{-{\frac {1}{4}}+{\frac {1}{4}\sqrt {1-4\,a-4\,b}}} \right \} \] 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),'implicit')
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))