ODE
\[ x^4 y''(x)+\left (1-2 x^2\right ) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0421556 (sec), leaf count = 47
\[\left \{\left \{y(x)\to c_1 e^{i/x} x (x-i)+\frac {1}{2} c_2 e^{-i/x} (1-i x) x\right \}\right \}\]
Maple ✓
cpu = 0.074 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) =x \left ( \left ( {\it \_C1}\,x+{\it \_C2} \right ) \cos \left ( {x}^{-1} \right ) -\sin \left ( {x}^{-1} \right ) \left ( {\it \_C2}\,x-{\it \_C1} \right ) \right ) \right \} \] Mathematica raw input
DSolve[(1 - 2*x^2)*y[x] + x^4*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^(I/x)*x*(-I + x)*C[1] + ((1 - I*x)*x*C[2])/(2*E^(I/x))}}
Maple raw input
dsolve(x^4*diff(diff(y(x),x),x)+(-2*x^2+1)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x*((_C1*x+_C2)*cos(1/x)-sin(1/x)*(_C2*x-_C1))