ODE
\[ -\left (2-x^2\right ) y'(x)+(2-x) x y''(x)+2 (1-x) y(x)=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.186946 (sec), leaf count = 18
\[\left \{\left \{y(x)\to c_2 x^2+c_1 e^x\right \}\right \}\]
Maple ✓
cpu = 0.068 (sec), leaf count = 14
\[[y \left (x \right ) = x^{2} \textit {\_C1} +\textit {\_C2} \,{\mathrm e}^{x}]\] Mathematica raw input
DSolve[2*(1 - x)*y[x] - (2 - x^2)*y'[x] + (2 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> E^x*C[1] + x^2*C[2]}}
Maple raw input
dsolve(x*(2-x)*diff(diff(y(x),x),x)-(-x^2+2)*diff(y(x),x)+2*(1-x)*y(x) = 0, y(x))
Maple raw output
[y(x) = x^2*_C1+_C2*exp(x)]