ODE
\[ \left (4 b-a^2\right ) y(x)+4 x^6 y''(x)+12 x^5 y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.02276 (sec), leaf count = 55
\[\left \{\left \{y(x)\to c_1 \cos \left (\frac {\sqrt {4 b-a^2}}{4 x^2}\right )-c_2 \sin \left (\frac {\sqrt {4 b-a^2}}{4 x^2}\right )\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 43
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sin \left ( {\frac {1}{4\,{x}^{2}}\sqrt {-{a}^{2}+4\,b}} \right ) +{\it \_C2}\,\cos \left ( {\frac {1}{4\,{x}^{2}}\sqrt {-{a}^{2}+4\,b}} \right ) \right \} \] Mathematica raw input
DSolve[(-a^2 + 4*b)*y[x] + 12*x^5*y'[x] + 4*x^6*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[1]*Cos[Sqrt[-a^2 + 4*b]/(4*x^2)] - C[2]*Sin[Sqrt[-a^2 + 4*b]/(4*x^2)]}}
Maple raw input
dsolve(4*x^6*diff(diff(y(x),x),x)+12*x^5*diff(y(x),x)+(-a^2+4*b)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1*sin(1/4*(-a^2+4*b)^(1/2)/x^2)+_C2*cos(1/4*(-a^2+4*b)^(1/2)/x^2)