ODE
\[ (m+1) a(m) x^m y(x)+x^2 y''(x)+x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.183536 (sec), leaf count = 63
\[\left \{\left \{y(x)\to c_1 I_0\left (\frac {2 \sqrt {x^m} \sqrt {-((m+1) a(m))}}{m}\right )+2 c_2 K_0\left (\frac {2 \sqrt {x^m} \sqrt {-((m+1) a(m))}}{m}\right )\right \}\right \}\]
Maple ✓
cpu = 0.25 (sec), leaf count = 49
\[\left [y \left (x \right ) = \textit {\_C1} \BesselJ \left (0, \frac {2 \sqrt {\left (m +1\right ) a \left (m \right )}\, x^{\frac {m}{2}}}{m}\right )+\textit {\_C2} \BesselY \left (0, \frac {2 \sqrt {\left (m +1\right ) a \left (m \right )}\, x^{\frac {m}{2}}}{m}\right )\right ]\] Mathematica raw input
DSolve[(1 + m)*x^m*a[m]*y[x] + x*y'[x] + x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> BesselI[0, (2*Sqrt[x^m]*Sqrt[-((1 + m)*a[m])])/m]*C[1] + 2*BesselK[0, (2*Sqrt[x^m]*Sqrt[-((1 + m)*a[m])])/m]*C[2]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)+(m+1)*a(m)*x^m*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*BesselJ(0,2*((m+1)*a(m))^(1/2)*x^(1/2*m)/m)+_C2*BesselY(0,2*((m+1)*a(m))^(1/2)*x^(1/2*m)/m)]