4.28.43 \(x y''(x)-\left (1-x^2\right ) y'(x)=0\)

ODE
\[ x y''(x)-\left (1-x^2\right ) y'(x)=0 \] ODE Classification

[[_2nd_order, _missing_y]]

Book solution method
TO DO

Mathematica
cpu = 0.00819388 (sec), leaf count = 21

\[\left \{\left \{y(x)\to c_2-c_1 e^{-\frac {x^2}{2}}\right \}\right \}\]

Maple
cpu = 0.01 (sec), leaf count = 14

\[ \left \{ y \left ( x \right ) ={\it \_C1}+{{\rm e}^{-{\frac {{x}^{2}}{2}}}}{\it \_C2} \right \} \] Mathematica raw input

DSolve[-((1 - x^2)*y'[x]) + x*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> -(C[1]/E^(x^2/2)) + C[2]}}

Maple raw input

dsolve(x*diff(diff(y(x),x),x)-(-x^2+1)*diff(y(x),x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1+exp(-1/2*x^2)*_C2