ODE
\[ \left (1-x^2\right ) y''(x)-\left (x^2+1\right ) y(x)-4 x y'(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0268193 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {e^{-i x} \left (2 c_1-i c_2 e^{2 i x}\right )}{2 \left (x^2-1\right )}\right \}\right \}\]
Maple ✓
cpu = 0.04 (sec), leaf count = 21
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,\sin \left ( x \right ) +{\it \_C2}\,\cos \left ( x \right ) }{{x}^{2}-1}} \right \} \] Mathematica raw input
DSolve[-((1 + x^2)*y[x]) - 4*x*y'[x] + (1 - x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> (2*C[1] - I*E^((2*I)*x)*C[2])/(2*E^(I*x)*(-1 + x^2))}}
Maple raw input
dsolve((-x^2+1)*diff(diff(y(x),x),x)-4*x*diff(y(x),x)-(x^2+1)*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = (_C1*sin(x)+_C2*cos(x))/(x^2-1)