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

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.0111911 (sec), leaf count = 30

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

Maple
cpu = 2.933 (sec), leaf count = 47

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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