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 = 0.0103336 (sec), leaf count = 22
\[\left \{\left \{y(x)\to c_1 J_p(a x)+c_2 Y_p(a x)\right \}\right \}\]
Maple ✓
cpu = 0.036 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{p}\left (ax\right )}+{\it \_C2}\,{{\sl Y}_{p}\left (ax\right )} \right \} \] 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),'implicit')
Maple raw output
y(x) = _C1*BesselJ(p,a*x)+_C2*BesselY(p,a*x)