ODE
\[ \left (1-x^2\right ) y'(x)+x y(x)-x=0 \] ODE Classification
[_separable]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.178071 (sec), leaf count = 19
\[\left \{\left \{y(x)\to 1+c_1 \sqrt {x^2-1}\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 18
\[\left [y \left (x \right ) = \sqrt {x -1}\, \sqrt {1+x}\, \textit {\_C1} +1\right ]\] Mathematica raw input
DSolve[-x + x*y[x] + (1 - x^2)*y'[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> 1 + Sqrt[-1 + x^2]*C[1]}}
Maple raw input
dsolve((-x^2+1)*diff(y(x),x)-x+x*y(x) = 0, y(x))
Maple raw output
[y(x) = (x-1)^(1/2)*(1+x)^(1/2)*_C1+1]