ODE
\[ x^{2 a} y''(x)+a x^{2 a-1} y'(x)+(1-a)^2 y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.195116 (sec), leaf count = 29
\[\left \{\left \{y(x)\to c_1 \cos \left (x^{1-a}\right )-c_2 \sin \left (x^{1-a}\right )\right \}\right \}\]
Maple ✓
cpu = 0.1 (sec), leaf count = 30
\[[y \left (x \right ) = \sin \left (x^{1-a}\right ) \textit {\_C1} +\textit {\_C2} \cos \left (x^{1-a} \mathrm {csgn}\left (a -1\right )\right )]\] Mathematica raw input
DSolve[(1 - a)^2*y[x] + a*x^(-1 + 2*a)*y'[x] + x^(2*a)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cos[x^(1 - a)] - C[2]*Sin[x^(1 - a)]}}
Maple raw input
dsolve(x^(2*a)*diff(diff(y(x),x),x)+a*x^(2*a-1)*diff(y(x),x)+(1-a)^2*y(x) = 0, y(x))
Maple raw output
[y(x) = sin(x^(1-a))*_C1+_C2*cos(x^(1-a)*csgn(a-1))]