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