ODE
\[ 2 (1-x) x y''(x)+(x+1) y'(x)-y(x)=0 \] ODE Classification
[_Jacobi]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0312438 (sec), leaf count = 21
\[\left \{\left \{y(x)\to c_1 \sqrt {x}-2 c_2 (x+1)\right \}\right \}\]
Maple ✓
cpu = 0.019 (sec), leaf count = 14
\[ \left \{ y \left ( x \right ) =\sqrt {x}{\it \_C2}+{\it \_C1}\,x+{\it \_C1} \right \} \] Mathematica raw input
DSolve[-y[x] + (1 + x)*y'[x] + 2*(1 - x)*x*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> Sqrt[x]*C[1] - 2*(1 + x)*C[2]}}
Maple raw input
dsolve(2*x*(1-x)*diff(diff(y(x),x),x)+(1+x)*diff(y(x),x)-y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = x^(1/2)*_C2+_C1*x+_C1