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 = 0.0103287 (sec), leaf count = 32

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

Maple
cpu = 0.011 (sec), leaf count = 48

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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