4.31.48 $(1-x^2)y^{″}(x)-(x^2+1)y(x)-4x{y}^{\prime }(x)=0$

ODE
$$(1-x^2)y^{″}(x)-(x^2+1)y(x)-4x{y}^{\prime }(x)=0$$ ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0268193 (sec), leaf count = 41

$$\left\{\{y(x)\to \frac{e^{-ix}(2c_1-i{c}_2{e}^{2ix})}{2(x^2-1)}\}\right\}$$

Maple ✓
cpu = 0.04 (sec), leaf count = 21

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{2}\cos \left(x\right)}{x^2-1}\}$$ 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)