ODE
\[ -\left (a^2-x\right ) y(x)+4 x^2 y''(x)+4 x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.120159 (sec), leaf count = 38
\[\left \{\left \{y(x)\to c_1 \Gamma (1-a) J_{-a}\left (\sqrt {x}\right )+c_2 \Gamma (a+1) J_a\left (\sqrt {x}\right )\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{a}\left (\sqrt {x}\right )}+{\it \_C2}\,{{\sl Y}_{a}\left (\sqrt {x}\right )} \right \} \] Mathematica raw input
DSolve[-((a^2 - x)*y[x]) + 4*x*y'[x] + 4*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> BesselJ[-a, Sqrt[x]]*C[1]*Gamma[1 - a] + BesselJ[a, Sqrt[x]]*C[2]*Gamma[1 + a]}}
Maple raw input
dsolve(4*x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)-(a^2-x)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*BesselJ(a,x^(1/2))+_C2*BesselY(a,x^(1/2))