ODE
\[ 4 x^3 y'(x)+4 x^2 y''(x)-\left (3-2 x^2\right ) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.196993 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \frac {c_1 e^{-\frac {x^2}{2}}+c_2}{\sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.041 (sec), leaf count = 21
\[\left [y \left (x \right ) = \frac {{\mathrm e}^{-\frac {x^{2}}{2}} \textit {\_C1}}{\sqrt {x}}+\frac {\textit {\_C2}}{\sqrt {x}}\right ]\] Mathematica raw input
DSolve[-((3 - 2*x^2)*y[x]) + 4*x^3*y'[x] + 4*x^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (C[1]/E^(x^2/2) + C[2])/Sqrt[x]}}
Maple raw input
dsolve(4*x^2*diff(diff(y(x),x),x)+4*x^3*diff(y(x),x)-(-2*x^2+3)*y(x) = 0, y(x))
Maple raw output
[y(x) = exp(-1/2*x^2)/x^(1/2)*_C1+_C2/x^(1/2)]