##### 4.6.35 $$a+\left (1-x^2\right ) y'(x)-x y(x)=0$$

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.175072 (sec), leaf count = 57

$\left \{\left \{y(x)\to \frac {-a \log \left (1-\frac {x}{\sqrt {x^2-1}}\right )+a \log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+2 c_1}{2 \sqrt {x^2-1}}\right \}\right \}$

Maple
cpu = 0.008 (sec), leaf count = 48

$\left [y \left (x \right ) = \frac {a \sqrt {\left (x -1\right ) \left (1+x \right )}\, \ln \left (x +\sqrt {x^{2}-1}\right )}{\left (x -1\right ) \left (1+x \right )}+\frac {\textit {\_C1}}{\sqrt {x -1}\, \sqrt {1+x}}\right ]$ Mathematica raw input

DSolve[a - x*y[x] + (1 - x^2)*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (2*C[1] - a*Log[1 - x/Sqrt[-1 + x^2]] + a*Log[1 + x/Sqrt[-1 + x^2]])/(
2*Sqrt[-1 + x^2])}}

Maple raw input

dsolve((-x^2+1)*diff(y(x),x)+a-x*y(x) = 0, y(x))

Maple raw output

[y(x) = 1/(x-1)/(1+x)*a*((x-1)*(1+x))^(1/2)*ln(x+(x^2-1)^(1/2))+1/(x-1)^(1/2)/(1
+x)^(1/2)*_C1]