ODE
\[ -\left (p^2+x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0 \] ODE Classification
[[_Bessel, _modified]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.162821 (sec), leaf count = 26
\[\{\{y(x)\to c_1 J_p(-i x)+c_2 Y_p(-i x)\}\}\]
Maple ✓
cpu = 0.03 (sec), leaf count = 15
\[[y \left (x \right ) = \textit {\_C1} \BesselI \left (p , x\right )+\textit {\_C2} \BesselK \left (p , x\right )]\] Mathematica raw input
DSolve[-((p^2 + x^2)*y[x]) + x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> BesselJ[p, (-I)*x]*C[1] + BesselY[p, (-I)*x]*C[2]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-(p^2+x^2)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*BesselI(p,x)+_C2*BesselK(p,x)]