4.36.16 \(x^{2 a} y''(x)+a x^{2 a-1} y'(x)+(1-a)^2 y(x)=0\)

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 = 0.0329595 (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 = 0.025 (sec), leaf count = 30

\[ \left \{ y \left ( x \right ) =\sin \left ( {x}^{1-a} \right ) {\it \_C1}+{\it \_C2}\,\cos \left ( {x}^{1-a}{\it csgn} \left ( a-1 \right ) \right ) \right \} \] 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),'implicit')

Maple raw output

y(x) = sin(x^(1-a))*_C1+_C2*cos(x^(1-a)*csgn(a-1))