ODE
\[ -y(x) \left (p^2-a^2 x^2\right )+x^2 y''(x)+x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.180607 (sec), leaf count = 22
\[\{\{y(x)\to c_1 J_p(a x)+c_2 Y_p(a x)\}\}\]
Maple ✓
cpu = 0.041 (sec), leaf count = 19
\[[y \left (x \right ) = \textit {\_C1} \BesselJ \left (p , a x \right )+\textit {\_C2} \BesselY \left (p , a x \right )]\] Mathematica raw input
DSolve[-((p^2 - a^2*x^2)*y[x]) + x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> BesselJ[p, a*x]*C[1] + BesselY[p, a*x]*C[2]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-(-a^2*x^2+p^2)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*BesselJ(p,a*x)+_C2*BesselY(p,a*x)]