ODE
\[ a^2 x^{a-1} y(x)+x^{a+1} y''(x)+(1-2 a) x^a y'(x)=0 \] ODE Classification
[[_Emden, _Fowler]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.180536 (sec), leaf count = 18
\[\left \{\left \{y(x)\to x^a (a c_2 \log (x)+c_1)\right \}\right \}\]
Maple ✓
cpu = 0.108 (sec), leaf count = 17
\[[y \left (x \right ) = \textit {\_C1} \,x^{a}+\textit {\_C2} \,x^{a} \ln \left (x \right )]\] Mathematica raw input
DSolve[a^2*x^(-1 + a)*y[x] + (1 - 2*a)*x^a*y'[x] + x^(1 + a)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> x^a*(C[1] + a*C[2]*Log[x])}}
Maple raw input
dsolve(x^(1+a)*diff(diff(y(x),x),x)+(1-2*a)*x^a*diff(y(x),x)+a^2*x^(a-1)*y(x) = 0, y(x))
Maple raw output
[y(x) = _C1*x^a+_C2*x^a*ln(x)]