ODE
\[ -\left (p^2-x^2\right ) y(x)+x^2 y''(x)+x y'(x)=0 \] ODE Classification
[_Bessel]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0134756 (sec), leaf count = 18
\[\left \{\left \{y(x)\to c_1 J_p(x)+c_2 Y_p(x)\right \}\right \}\]
Maple ✓
cpu = 0.029 (sec), leaf count = 15
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl J}_{p}\left (x\right )}+{\it \_C2}\,{{\sl Y}_{p}\left (x\right )} \right \} \] 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, x]*C[1] + BesselY[p, 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),'implicit')
Maple raw output
y(x) = _C1*BesselJ(p,x)+_C2*BesselY(p,x)