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

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

[_separable]

Book solution method
Linear ODE

Mathematica
cpu = 0.00769271 (sec), leaf count = 19

\[\left \{\left \{y(x)\to c_1 \sqrt {x^2-1}+1\right \}\right \}\]

Maple
cpu = 0.012 (sec), leaf count = 18

\[ \left \{ y \relax (x ) =\sqrt {-1+x}\sqrt {1+x}{\it \_C1}+1 \right \} \] 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),'implicit')

Maple raw output

y(x) = (-1+x)^(1/2)*(1+x)^(1/2)*_C1+1